Usova E.Yu., Filatov A.Yu. Irkutsk State University Empirical study of compulsory motor liability insurance using the example of the insurance company "RESO-Garantia"

Insurance in Russia and other countries Insurance is a relationship to protect the property interests of individuals and legal entities in the event of insured events at the expense of funds generated from insurance premiums. The share of insurance premiums in GDP Russia is 2.5%, USA – 9%, France – 11%, UK – 16%. Insurance premium per capita Russia – $250, USA, France – $4 thousand, Great Britain – $6.5 thousand. The volume of the insurance market is ~ 1 trillion rubles. Growth rate is greater than GDP; in 2009 the fall (even excluding compulsory medical insurance) is less than that of GDP.

Insurance premiums and payments by type of insurance in 2008 Indicator name Insurance premiums Insurance payments Share of payments in premiums billion rubles % % Voluntary insurance Life insurance 194.0263.070.32 Personal insurance 10823.176131.520.56 Property insurance 31667.030.40 Liability insurance234.8631.380.13 Total: .42 Compulsory motor liability insurance8016.594811.130.60 Compulsory medical insurance 39481.420.95 Other81.5861.450.75 Total: .89

Insurance rates for compulsory motor liability insurance Increasing and decreasing coefficients: 1. Features of the territory where vehicles are used. 2.Nature of use of the car 3.Power of the vehicle. 4.Presence or absence of insurance payments in previous periods. 5.Driving experience and age of car users. 6. Period of seasonal use of the car. Basic rates are differentiated depending on the technical characteristics and design features of vehicles, which affect the likelihood of causing harm when using the vehicle, as well as the potential extent of this harm. On March 25, 2009, new tariffs for compulsory motor liability insurance were introduced! Analysis of tariff adjustments based on statistics on 20 thousand contracts of IC "RESO-Garantia", concluded in 2007 (all payments were made).

Basic tariffs for various types of vehicles Type of vehicle Current tariffs, rub. Estimated tariffs, rub. Profit at the current tariff Trailers for cars 39513.782767.20% Trailers for trucks 810225.36259.43% Tractors 89267.20% Buses, trolleybuses 2632.87% Passenger cars (individuals) 6629.44% Passenger cars (legal entities) ,33–1.10% Taxi, 69–67.25% Trucks (up to 16 tons) ,52–17.13% Trucks (over 16 tons) ,03121.01% 1. Taxi – the rate is significantly reduced, insurance company losses, unwillingness to insure. 2. Trailers for passenger cars (432 contracts) – the rate is too high, compulsory insurance has been cancelled.

Engine power factor By individual group Based on regression Power. engine, hp Calculation. net premium Coef. to Coef. with Calc. coefficient Actual/calc. to Actual/calc. with Calc. coefficient Actual/calc. to Actual/calc. c.731.71.60.9970.99%60.93% 1.4219.78%12.74% 1. Cars with low engine power (high share of domestic ones) – the coefficient is underestimated. 2.Powerful cars – overpriced. 3. The discrepancy between the current and calculated coefficients has decreased.

Age and experience coefficient Age and experience of the driver Frequency of fear. cases Calc. coefficient Coef. to Coef. with Actual/calc. to Actual/calc. with no restrictions 0.07632.041.51.7–26.55%–16.76% up to 22 years with experience up to 3 years 0.06741.801.31.7–27.92%–5.75% up to 22 years with over 3 years of experience0.03891.041.21.315.27%24.88% of 22 years with up to 3 years of experience0.07231.931.151.5–40.56%–22.47% of 22 years with over 3 years of experience0 , Simplification: we believe that the size of the average insurance payment does not depend on the age and length of service of the driver (only the frequency is important). This is acceptable, unlike base rates, engine power factors and territory. 1. Of experience and age, experience is a significant component. 2. Inexperienced drivers - the coefficient is underestimated (despite the increase). 3.No restrictions - the coefficient is underestimated (despite the increase). 4. Experienced young drivers – the coefficient is overestimated (the discrepancy has even increased slightly). 5.Gender influences loss ratio more strongly than age. The indicators are interconnected.

Bonus-malus coefficient Coefficient. bonus-malus Insurance premium Insurance premium without coefficient. Insurance payments Share of payments in premium Share taking into account regression Calculation. coefficient 0.42010.38820.48 0.44820.49400.61 0.58280.59970.74 0.74870.70550.79870, The company is most profitable to work with clients who have not been involved in an accident in previous years and who have a reduction factor . 2. There is a reserve for reducing the bonus-malus coefficient for these categories of drivers.

Construction of a theoretical law for the distribution of payments Lognorm.distribution. Exponential distribution Gamma distribution Fear. payments, thousand rubles Number of fear. cases Share of fear. cases Theor. probable Critical calculation Pearson Theoret. probable Critical calculation Pearson Theoret. probable Critical calculation Pearson 0– .3250.2210.049 0.3590.003 0.3370.000 10– .2970.4030.028 0.2300.020 0.2420.013 20– .1520.2050.013 0.1480.000 0.1570.000 30– .0650.0900.007 0.0950.009 0.0990.012 40– .0520.0410.003 0.0610.001 0.0620.002 50–6036 0.0400.0190, 022 0.0390.000 0.0390.000 60–7017 0.0190.0100.009 0.0250.002 0.0240.001 70–8015 0.0170.0050.027 0.0160.000 0.0150, 000 80–908 0.0090.0030.014 0.0100.000 0.0090.000 90– .0140.0020.109 0.0070.009 0.0060, –1106 0.0070.0010.038 0.0040 .001 0.0040, –1203 0.0030.0010.015 0.0030.000 0.0020, =0.333 =0.046 =0.045

Application of the theoretical law of distribution of payments Finding the probability of payments of an arbitrary given size: 1. Calculation of the tariff for DSAGO (extension of the liability limit to 420 thousand rubles). Taking into account the load of 20%, the calculated premium for the gamma distribution is ~ 90 rubles. 2. Calculation of correction factors for the franchise (exemption of insurance companies from compensation for losses not exceeding a specified amount). Franchise, ruble Discount, %1,987,3014,6723,06 3. Formation of insurance tariffs for voluntary types of insurance, in particular, for CASCO.

Pros and cons of the state setting of tariffs for compulsory motor liability insurance Pros: 1. Unification of insurance conditions and simplification of the policyholder's decision when choosing an insurance company. 2. The impossibility of dumping on the part of insurance companies in order to attract clients and subsequent failure to fulfill obligations. Disadvantages: 1. Possible discrepancy between insurance rates and economic realities and a wide range of unprofitability. 2. Slow response of tariff rates to changes in market conditions. 3. Insufficient differentiation of risks and poor consideration of the peculiarities of local insurance markets in tariffs. 4. The inability of the insurance company to attract less unprofitable clients on special terms.

Thank you for your attention!

3.3 Analysis of problems in CASCO insurance

In the realities of today's life, auto CASCO is everything that relates to the integrity and safety of the body, i.e. "sides" of a car. But today there are a number of problems with CASCO insurance, which are presented in Table 16.

Table16

Problems of CASCO insurance and ways to solve them

This table shows that there are a number of different problems with CASCO insurance, all of which, in my opinion, are very important because They all, to one degree or another, affect CASCO insurance, and this table already presents solutions to combat these problems.

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480 rub. | 150 UAH | $7.5 ", MOUSEOFF, FGCOLOR, "#FFFFCC",BGCOLOR, "#393939");" onMouseOut="return nd();"> Dissertation - 480 RUR, delivery 10 minutes, around the clock, seven days a week and holidays

Yarkova Olga Nikolaevna. Models and methods for assessing the solvency of an insurance company, taking into account investment and reinsurance (using the example of CASCO): dissertation... Candidate of Economic Sciences: 08.00.13 / Olga Nikolaevna Yarkova; [Place of defense: GOUVPO "Samara State Aerospace University"]. - Samara, 2010. - 183 p.: ill.

Introduction

Chapter 1 Risk models in insurance and methods for increasing the solvency of insurance companies 8

1.1 Risks in insurance 8

1.2 Methods for assessing solvency 16

1.3 Models for assessing solvency and approaches to improve it.29

Chapter 2 Study of the influence of risk process characteristics and assets on the probability of non-ruin 38

2.1 Study of the dependence of the probability of non-ruin on the initial capital 38

2.2 Study of the influence of asset characteristics on the solvency of an insurance company 51

2.3 Analysis of the influence of initial capital on the strategy of investing in risky or risk-free assets 57

Chapter 3 Formation of investment and reinsurance strategy 66

3.1 Analysis of the impact of diversification of investments in risky and risk-free assets on solvency 66

3.2 Formation of an investment strategy 75

3.3 The impact of reinsurance on solvency 82

Conclusion 96

List of sources used 98

Applications 106

Introduction to the work

Relevance of the research topic. Increasing competition, evidenced by a decrease in the share of leading insurance companies in the total volume of collected premiums (according to the Expert RA Rating Agency), and an increase in risks caused by the global financial crisis, give rise to high demands for an objective assessment of not only the solvency of insurance companies, under which Let us understand the positivity of the risk process, but also the tools that influence it. One of the tools to influence solvency is the equity capital of the insurance company, which can be increased through investment. The influence of equity capital on such a characteristic of solvency as the probability of non-ruin is devoted to the works of foreign and domestic authors F. Lundberg, G. Grandell, F. de Vilder, T. Anderson, X. Kramer, G.Sh. Tsitsiashvili. K. Segerdahl, J. Paulsen and H. Ggessing studied the dependence of solvency on the initial capital of an insurance company, taking into account the investment of available funds in risk-free assets. In the works of S. Brown, A.V. Melnikov and S. Asmussen analyzed the influence of initial capital on the probability of non-ruin of an insurance company, taking into account the investment of available funds in risky assets.

Another option to increase the probability of non-ruin is reinsurance. In the works of H. Schmidli and K. Hipp, an estimate was obtained of the dependence of the probability of failure of an insurance company on the initial capital, taking into account reinsurance and investment in risky assets, but with strict assumptions about the nature of the distribution of payments and large values ​​of the initial capital.

Thus, it can be stated that the works of domestic and foreign authors do not pay attention to the issues of modeling the dependence of the probability of non-ruin of insurance companies on such characteristics of the risk process and assets as the relative risk premium, the profitability of risky and risk-free assets, the volatility of prices of a risky asset, the share of investment in risky (risk-free) assets, the volume of own retention during reinsurance, etc. The scientific and practical significance and insufficient development of these issues of assessing the solvency of insurance organizations determined the choice of topic and structure of the study.

The purpose of the study is to improve methods for assessing the probability of non-ruin in the conditions of investment and reinsurance when solving the problem of increasing the solvency of an insurance company.

To achieve this goal, the following tasks were set and solved:

analysis of existing methods and models for assessing the solvency of insurance companies;

Modeling the relationship between the probability of non-ruin and the characteristics of the risk process, assets, the volume of investment and reinsurance;

Development of a methodology for forming investment strategies

In risk-free assets;

In risky assets;

In risky and risk-free assets;

Development of a methodology for forming reinsurance strategies in various investment conditions.

The object of the study is the probability of non-ruin, as a characteristic of the solvency of the insurance company.

The subject of the study is methods and models for assessing the probability of failure of an insurance company. Area of ​​study - 1.6. Mathematical analysis and modeling of processes in the financial sector of the economy, development of the method of financial mathematics and actuarial calculations.

Theoretical and methodological basis of the research The works of domestic and foreign authors on insurance and actuarial mathematics, probability theory, random processes, mathematical statistics, and numerical analysis were used as the theoretical basis of the dissertation work. Numerical modeling was implemented using the Delphi 7.0 software development environment.

Data from the insurance company RESO-Garantia were used as the information base for the study.

The scientific novelty lies in the modeling of the dependence of the probability of non-ruin on the characteristics of the risk process, risky and risk-free assets, which makes it possible to formulate investment and reinsurance strategies to increase the solvency of the insurance company.

The most significant scientific results:

a procedure for mathematical modeling of the relationships between the probability of non-ruin and the relative risk premium, the relative risk premium and initial capital, the probability of non-ruin and the profitability of risky and risk-free assets, the probability of non-ruin and the volatility of prices of a risky asset, etc., which allows us to quantify the impact of the characteristics of the risk process and assets on the solvency characteristics of the insurance company;

A methodology has been developed for developing investment strategies in risky and/or risk-free assets based on constructed models characterizing the relationship between the probability of non-ruin and the volume of investment; the volume of investment and initial capital, the use of which makes it possible to increase the solvency of the insurance company;

A methodology has been proposed for the formation of reinsurance strategies in various investment conditions based on constructed models that describe the dependencies between solvency characteristics and the volume of own retention, the implementation of which makes it possible to increase the likelihood of the insurance company not going bankrupt.

Practical significance The results of the study were accepted for implementation in the insurance company RESO-Garantiya (Orenburg branch) and are used when considering issues related to ensuring a high level of non-ruin. The theoretical and practical results obtained during the study are used in the course of the academic discipline “Insurance and Actuarial Calculations”.

Approbation of the work The main theoretical and practical provisions of the dissertation work were reported and discussed at conferences:

All-Russian scientific and practical conference “Interaction of the real and financial sectors in a transformational economy” (Orenburg, State Educational Institution OSU, 2008);

All-Russian Scientific and Practical Conference “Financial and Actuarial Mathematics” (Neftekamsk, NFBash State University, 2009);

All-Russian scientific and practical conference "Multidisciplinary University as a regional center of education and science" (Orenburg, State Educational Institution OSU, 2009).

Structure and scope of work The dissertation consists of an introduction, three chapters, a conclusion, a list of references and appendices. The appendices contain information and reference materials that illustrate and complement the main content of the study. The dissertation is presented on 212 pages of typewritten text, contains 84 tables and 56 figures. The list of references includes 93 titles of works by domestic and foreign authors. The applications are presented on 107 pages.

The first chapter, “Risk models in insurance and methods for increasing the solvency of insurance companies,” reveals the economic essence of insurance as one of the risk management methods, describes models and methods for assessing the probability of non-ruin, and considers approaches to increasing the solvency of an insurance company.

In the second chapter, “Study of the influence of the characteristics of the risk process and assets on the probability of non-ruin,” the dependence of the probability of non-ruin of an insurance company on the initial capital in the Poisson model of collective risk is constructed, taking into account investment in either risky or risk-free assets. A procedure for modeling the relationships between the probability of non-ruin and the relative risk premium, the relative risk premium and initial capital, the probability of non-ruin and the return on risky and risk-free assets, the probability of non-ruin and the volatility of the prices of a risky asset is proposed and implemented. A methodology has been developed for developing an investment strategy in risky or risk-free assets.

In the third chapter, “Formation of investment and reinsurance strategies,” the dependence of the probability of non-ruin on the initial capital in terms of investing in risky and risk-free assets is constructed. Modeling of the relationship between the probability of non-ruin and the volume of investment in risky and risk-free assets was carried out; volume of investment and initial capital of the insurance company. A methodology for forming reinsurance strategies in various investment conditions is proposed.

Models for assessing solvency and approaches to increasing it

To implement its main function - making payments upon the occurrence of insured events - the insurance company must have special monetary resources that determine its capital. The capital (reserve) of an insurance organization consists of two main parts - own capital and attracted capital, and the attracted part of the capital largely prevails over its own. This is due to the industry specifics of insurance. The activities of an insurance company are based on the creation of funds, the source of which is the funds of policyholders received in the form of insurance contributions (premiums). They do not belong to the insurer. These funds are only temporarily, for the period of validity of the insurance contracts, at the disposal of the insurance company, after which they are used to pay the insured amount or are converted into an income base (subject to the break-even completion of the contract), or are returned to the policyholders in the part provided for by the terms of the contract (bonus). Thus, the capital of the insurance company Y, at time t is equal to S(t) - the amount of payments made by the insurance company at time /; n(t) - premiums collected by time t. Process (1.1) is also called the risk process of the insurance company.

The formation and use of capital is one of the main aspects of the activities of insurance organizations, aimed at ensuring solvency. An additional source of profit for the insurer, in addition to profit from insurance operations, is investment income. Profitable investment activity allows the insurer to reduce the tariff, which is of interest to both insurers and policyholders. Not only the insurer’s income, but also its solvency depends on the efficiency and reliability of the placement of temporarily available funds. Thus, until 2005, the average return on investment of insurance companies lagged behind the rate of inflation and there was an increase in the number of insolvent insurers. In 2006, as of January 1, 2007, 14% of the total number of registered insurers had their license revoked. The inclusion of Russia in global integration processes forces insurance companies to approach the conditions of world standards, and the increase in financial risks in a crisis and increasing competition, as evidenced by data from the Expert RA agency, give rise to high demands for an objective assessment of the solvency of insurance companies.

A number of indicators are used to study the solvency of insurance companies. Some of these indicators are normative in nature and are established and controlled by government bodies, others are advisory. In Russia, the following indicators are used: minimum level of authorized capital; regulatory solvency margin; the amount of required insurance reserves; standards for investment activities, etc. All these indicators reflect only certain aspects of the activities of insurance companies and are not quantitative characteristics of the company’s solvency. In the works, as a measure of the solvency of the insurance company, the probability of non-ruin p(ii) = P\Yl 0), or the probability of ruin y/(u) = l-P(Yt 0), is used as a characteristic of the opposite event, which are a measure of the risk of the functioning of the insurance company characterizing the solvency properties of the company as a whole or individual portfolios of contracts. The concept of "ruin" means the excess of payments over receipts and reserves. However, a deficit of the latter does not mean bankruptcy of the insurance company, since the company can use other sources of repayment of the deficit, for example, a loan. In risk theory, ruin (falling assets to zero) should be understood as some indicator signaling financial trouble. Sometimes ruin is understood as a reduction in capital to a certain positive minimum - the minimum regulatory level (if the capital is less than the regulatory level, the activities of the insurer are suspended by regulatory authorities). This approach is typical for EU countries. That is, the probability of ruin (or the probability of non-ruin) is a deterministic characteristic of solvency.

We will be interested in the dependence of the probability of ruin on the initial capital, relative risk premium, etc. Calculating the probability of ruin involves building models of individual or collective risk for the company as a whole or for individual portfolios of contracts. An individual risk model is characterized by the fact that all insured objects have the same characteristics, such as the probability of an insured event, the distribution of a possible insured loss, the terms and conditions of insurance. The insurance company compensates for damage only from funds received as insurance premiums. The individual risk model assumes that losses for each risk unit are independent and equally distributed. This assumption can be made in the case when insured losses for each insurance object are caused by different, unrelated reasons. This is a natural requirement in life insurance, however, it is not typical for other types of insurance. The information content of such a model is low, since factors that can simultaneously influence many risks in a group are not taken into account. In addition, the individual risk model is a static model of insurance risk, where the risk is modeled by only one random variable, namely the total insured loss for a group of risks, and static models provide a limited understanding of risk. Modification of the individual risk model is recommended by Rosstrakhnadzor when calculating tariff rates for risky types of insurance, due to the fact that it is the only analysis tool if statistical data is presented in aggregate form. The collective risk model most fully reflects real phenomena in insurance. With its help, you can achieve greater dynamics when managing the company's risk.

Study of the influence of asset characteristics on the solvency of an insurance company

In our example, an insurance company investing all available funds in a risk-free asset with a profitability of 0.13, with R = 3.82 claims/day, 0 = 60% and = 65%, to achieve a probability of non-ruin of 0.95, it is necessary to have an initial capital of 320 thousand rubles. and transfer 20% of risks to reinsurance. Similar calculations can be carried out for other model parameters.

The dependencies between the probability of non-ruin of the insurance company and the volume of own retention, calculated similarly, in the case of investing 50% of available funds in risky assets with a yield of 0.4 and price volatility of 0.25 and 50% of available funds in risk-free assets with a yield of 0.13, are presented in Table I. 14 of the Appendix And (family of solutions to problem (3.15) in tables Zh.30-Zh.32 of appendix G, interpolation splines in table K.20 of appendix K). Dependency graphs constructed for various values ​​of the relative risk premium of the reinsurer a) = 65%; b) = 75%; c) , = 85% are presented in Figure 3.15, and the RMNC approximations are given below:

For the given characteristics of the risk process, an insurance company with an initial capital of 350 thousand rubles. and investment strategies in risky (// = 0.4, st = 0.25) and risk-free (r = 0.13) assets (0.5, 0.5), respectively, to achieve a probability of non-ruin of 0.95, it is necessary to reinsure 7.5% of risks if the relative risk premium of the assignor is 60%, and relative risk premium of the reinsurer is 85%), or 5% of risks if the relative risk premium of the reinsurer is 65%. The relationships between the initial capital of the insurance company and the volume of own retention are calculated similarly for p = 0.95, in the case of investing 50%) of available funds in risky assets with a yield of 0.4 and price volatility of 0.25 and 50% of available funds in risk-free assets with a yield of 0.13. Graphs of calculated values ​​(Table I. 15) and interpolation splines for given parameters of the risk process (/3 = 0.5, r = 0.13, a = 0.5, // = 0.4, sr = 0.25, R = 3.82 claims/day, 0 = 60%, and =350 thousand rubles), (Appendix K, table K.21) are shown in Figure 3.16. own deduction, p = 0.5, r = 0.13, a = 0.5, /l = 0.4, a = 0.25, A = 3.82 claims/day, b = 60%, p = 0.95, for a) = 65%; b) = 75%; c) = 85%. Such dependencies will allow the insurance company to formulate a reinsurance strategy taking into account the characteristics of the assets. For example, to ensure a probability of non-ruin of 0.95 for an insurance company with an initial capital of 320 thousand rubles. it is necessary to invest 50% of available funds in risky assets with a yield of 0.4 and price volatility of 0.25, 50% of available funds in risk-free assets with a yield of 0.13 and give 15% of risks for reinsurance if the relative risk premium of the reinsurer is 0.65. Thus, we have quantitatively assessed the impact on the probability of not ruining the characteristics of assets, the volume of investment in risky and risk-free assets, which will allow us to formulate a strategy for investing in risky and risk-free assets depending on the size of the initial capital. In addition, a methodology for forming a reinsurance strategy in various investment conditions is proposed and demonstrated using the example of CASCO. All calculations presented in the work were obtained numerically using the automated software package “Analysis of the Solvency of an Insurance Company” (Appendix L). Conclusion The analysis of models and methods for assessing the solvency of an insurance company allowed us to conclude that there has been no research into the quantitative assessment of the impact on the probability of non-ruin of such characteristics as the relative risk premium, the profitability of risky and risk-free assets, the volatility of prices of a risky asset, the share of investment in risky and risk-free assets, the volume of own reinsurance retentions. The work proposes and implements a procedure for modeling the relationships between the characteristics of the solvency of an insurance company and the characteristics of the risk process, assets, volume of investment and reinsurance, allowing: - to quantify the size of the relative risk premium that provides a given probability of non-ruin with a fixed initial capital in various investment conditions; - quantify the size of the relative risk premium depending on the size of the initial capital, guaranteeing a fixed level of probability of non-ruin in various investment conditions; - quantitatively assess the impact of the profitability of a risk-free asset, the profitability of a risky asset, the volatility of prices of a risky asset on the probability of non-ruin of the insurance company. A methodology for developing investment strategies in risky assets has been developed and implemented; into risk-free assets; into risky and risk-free assets that provide the required level of probability of non-ruin, depending on the relationship between the characteristics of the assets and the characteristics of the risk process.

Analysis of the influence of initial capital on the strategy of investing in risky or risk-free assets

There are three main ways to influence risk - reduction, preservation and transfer. Risk reduction refers to a reduction in either the amount of possible damage or the likelihood of adverse events occurring. The preservation group includes self-insurance, i.e. creation of special reserve funds (self-insurance funds or risk fund) from which compensation for losses will be made in the event of unfavorable situations. Risk transfer means transferring responsibility for the risk to third parties, while maintaining the level of risk. This group includes insurance, which involves transferring risk to an insurance company for a fee, as well as various types of guarantees, financial guarantees, etc.

Let us define insurance as “a set of social relations associated with the formation of an insurance fund through contributions made by participants in its creation, with its centralization in organizations carrying out insurance operations and with its use to cover damage or make other payments to persons in respect of whom insurance is carried out.” , in the event of the occurrence of predetermined random events.” An insurance contract is called a policy. If the policy has been tendered for payment, the insurer is said to have received the claim; If the insurance situation does not arise, the policyholder loses the premium. The insurance company has numerous obligations and rights under the insurance contract. The insurer's responsibilities are divided into obligations to bear the risk and to pay insurance compensation (sum insured).

To implement its main function - making payments upon the occurrence of insured events - the insurance company must have special monetary resources that determine its capital. The capital (reserve) of an insurance organization consists of two main parts - own capital and attracted capital, and the attracted part of the capital largely prevails over its own. This is due to the industry specifics of insurance. The activities of an insurance company are based on the creation of funds, the source of which is the funds of policyholders received in the form of insurance contributions (premiums). They do not belong to the insurer. These funds are only temporarily, for the period of validity of the insurance contracts, at the disposal of the insurance company, after which they are used to pay the insured amount or are converted into an income base (subject to the break-even completion of the contract), or are returned to the policyholders in the part provided for by the terms of the contract (bonus). Thus, the capital of insurance company Y, at time t is equal to

Thus, studies of the solvency of insurance companies, which take into account investments in risky and risk-free assets, are characterized by both assumptions about the nature of the distribution of payment amounts and the lack of research into the influence on the solvency of such asset characteristics as the profitability of a risky and risk-free asset and the volatility of prices of a risky asset.

If the investment activities and financial capabilities of the insurer do not allow achieving the desired level of solvency, insurance companies resort to risk redistribution. Reinsurance is an important link in ensuring the solvency of the insurer. The need for reinsurance is due to the fact that: 1) small insurance companies do not have enough of their own funds to ensure a high level of non-ruin; 2) insurance companies do not always have the opportunity to create a perfectly balanced portfolio, due to the small number of insurance objects or the presence of large risks in the portfolio; 3) even with a careful selection of risks accepted for insurance, the insurer cannot create a portfolio of insurance objects that are completely independent from each other, since insurance compensates for losses arising from various types of dangers to which the insured objects may be exposed simultaneously during the occurrence of catastrophes; 4) economic development and scientific and technological progress lead to a high concentration of material assets and, as a consequence, to an increase in insurance amounts for a large number of insurance objects (the cost of transported goods increases, the cost of aircraft, ships, etc. increases). Insurance companies cannot accept such large risks for insurance without having reinsurance coverage. In some cases, insurance costs are so high (or dangerous) that the reserves of individual insurance companies are insufficient to provide full coverage. Reinsurance agreement is an agreement under which one party (the assignor) transfers the insurance risk (group of risks) in full or in part to the other party - the reinsurer. The insurer transferring the risk is called the assignor. The reinsurer undertakes to compensate the cedant for the corresponding part of the insurance compensation. Reinsurance ensures secondary redistribution of risk, thereby contributing to the quantitative and qualitative equalization of the insurance portfolio, which, in turn, makes it possible to accept unique and expensive risks for insurance. Let's consider a special case of reinsurance - proportional, in which the reinsurer's payments depend on the insurance payments for each claim, i.e. One of the ways to determine the optimal, from the insurer's point of view, volumes of reinsurance is based on making a decision based on a compromise between expected income and security. The reinsurer, when accepting the risk, charges a premium from the cedant. The rate of receipt of reinsurer's premiums is related to the relative risk premium by the ratio: where is the relative risk premium of the reinsurer. Then, the rate of receipt of premiums received by the assignor after reinsurance can be written as follows: In the works, it is proposed to use the Lundberg coefficient as an indicator of the reliability of the insurance company. If reinsurance premiums are paid continuously, with intensity c"er, then the Lundberg coefficient Rh for a direct insurer that has entered into a proportional reinsurance agreement is the smallest positive root of the equation. Based on equation (1.39), it is proposed to build a dependence of the Lundberg coefficient, reflecting the level of reliability of the insurance company, on the volume risk transferred to reinsurance. Preference is given to such a volume of risk that will provide the insurance company with the maximum value of Rh and the greatest income for the assignor. In the works of H. Schmidli and Z. Hipp, an assessment of the probability of ruin, taking into account investment and reinsurance, is sought as a solution to the Cauchy problem below: Based on (1.41), it is possible to determine the behavior strategy of the insurance company, providing the optimal combination of income and the probability of ruin.As in the case of using formula (1.10) to estimate the probability of ruin, the described methods can be applied only in the case when the distribution of payment amounts is a distribution with a light tail. Models (1.39), (1.41) provide exact solutions only in cases with distributions of payout sizes close to exponential.

Analysis of the impact of diversification of investments in risky and risk-free assets on solvency

Graphs of the dependence of the probability of non-ruin on the initial capital for the cases: a) without investment; b) with investment in risk-free assets g-0.13; c) with investment in risky assets /l = 0.4, a - 0.25, with e thousand rubles,

I - 3.82 ISK/day, s = 196.5 thousand rubles/day, I = 0.1 thousand rubles. Thus, we have the opportunity to formulate an investment strategy, depending on the size of the initial capital, with fixed parameters of the risk process, providing a higher level of probability of non-ruin. So, for example, investing in risky assets (// = 0.4; a = 0.25) allows you to achieve a probability of non-ruin of 0.95 with an initial capital value of 386.4 thousand rubles, when investing in risk-free assets (r = 0.13) a probability of not ruining 0.95 is achieved with an initial capital value of capital is 391.8 thousand rubles, and in the absence of investment, 447.3 thousand rubles are required. In the above case, with initial capital values ​​less than 444 thousand rubles. a higher probability of non-ruin is provided by risky assets, with values ​​of initial capital of more than 444 thousand rubles - risk-free.

In addition to the problem of estimating the dependence of the probability of non-ruin on the initial capital for fixed values ​​of the parameters of the collective risk model, it is of interest to estimate the dependence of the relative risk premium that provides a given level of probability of non-ruin on the size of the initial capital. Given the ratio

Problem (2.6) was solved numerically for various values ​​in (Appendix G, Table G.2 - G.4), and from the numerical solution of the equations (p(u 19) = p, where cp is the given level of probability of non-ruin, we obtained the values ​​of the initial capital and, which are presented in Appendix I (Table IL) for av = 0.95. The dependencies presented in Figure 2.4 were approximated by 3rd order splines (Appendix K, Table K.1). For clarity, we approximated them with generalized polynomials according to the system functions (n/SO)1",/ = 0.1..5 using the recurrent least squares method. In the illustrated case (R = 3.82 isks/day, Ф = 0.95) the approximations take the form: Figure 2.4 - Relationships between the relative risk premium and initial capital for cases: a) without investment, b) with investment in risk-free assets with a return of 0.13, c) with investment in risky assets /l = 0L, a = 0.25, with R = 3.82 claims/day, (p = 0.95 Such dependencies make it possible to determine the value of the relative risk premium, which will provide a given level of probability of non-ruin, depending on the size of the initial capital. So, for example: an insurance company with an initial capital of 400 thousand rubles. to ensure a probability of non-ruin of 0.95, it is necessary to set a relative risk premium of 71% in the absence of investment. Investing in risk-free assets with a return of 0.13 allows you to reduce the risk premium to 57.5%, with the same probability of non-ruin. Investing in risky assets with a return of 0.4 and a volatility of 0.25 allows you to reduce the relative risk premium to 55.5%. Let's assume that the insurance company has initial capital and wants to increase the probability of non-ruin due to the relative risk premium. For various values ​​of β, using the family of solutions to problem (2.6), we found p(i/β) (Appendix G, table G.2 - G.4) and plotted the dependence of the probability of non-ruin on the relative risk premium for a fixed value of the initial capital. Dependence of the probability of non-ruin on the relative risk premium for a fixed amount of initial capital and =350 thousand rubles. under various investment conditions are presented in Table I.2 (Appendix I; in the form of 3rd order splines in Appendix K, Table K.2). Approximations of the dependence of the probability of non-ruin on the relative risk premium, constructed for the given parameters of the risk process (R = 3.82 claims/day, m = 350 thousand rubles) using the recurrent least squares method, are presented below (2. 8), and the corresponding graphs in Figure 2.5.

Publication date: 10/28/2017 11:37

The first part of the thesis in psychology is a theoretical study. It involves studying literature on the topic of research, summarizing the material, its analysis and structured presentation.

Graduate theses in many humanities disciplines contain only empirical research. But in psychology, researchers strive to test their theories in practice. Therefore, the second part of the coursework, diploma and master's work in psychology is an empirical study.

What is empirical research in psychology

The term "empirical" is synonymous with the word practical, related to experience. Therefore, the second chapter of a diploma or coursework in psychology is also called “Practical Chapter” or “Experimental Chapter”.

The logic of the final work in psychology is as follows:

• First, the student studies what other researchers have done on his chosen topic. Gets acquainted with theoretical models of psychological phenomena, as well as the results of empirical research.
• Based on theoretical analysis of other people's work and his own ideas, the student develops a plan for his own empirical research.
• Next, the student psychologist conducts an empirical study, analyzes its results and draws conclusions.

What is the essence of empirical research in psychology?

Its main feature is that it allows you to study the patterns of the human psyche, patterns of thinking, emotional life, behavior, etc.

The main instrument of empirical research in psychology is the tools of psychological diagnostics - tests, questionnaires, questionnaires, etc. With their help, the research psychologist obtains empirical data, subjects them to mathematical analysis and, on its basis, draws conclusions about psychological patterns.

The results of empirical research in psychology claim the status of a psychological law or pattern. This brings psychology closer to the exact sciences, for example, physics.

However, in psychology there are many theories and models that are actively used in the practice of psychotherapy and counseling. But these models have not been empirically tested. However, the lack of empirical validity does not make these theories any less valuable. This fact reflects that psychology belongs to the humanities, where it is impossible to obtain accurate knowledge about an object.

Structure of the empirical study

The structure of empirical research is reflected in the first paragraph of the second (practical) chapter of a course, diploma or master's thesis in psychology and includes the following elements.

Purpose of empirical research, as a rule, coincides with the purpose of the entire work. Most often, this goal can be associated either with identifying relationships between psychological indicators, or with identifying differences in the severity of psychological parameters in two groups of subjects, divided by some criterion.

Objectives of empirical research reflect the sequence of steps that must be taken to achieve the goal of empirical research. For example, they may include:

1. Selection of psychodiagnostic techniques.
2. Sampling of empirical research.
3. Conducting psychodiagnostics and compiling a summary table of the results of psychological testing.
4. Qualitative analysis of the obtained data.
5. Statistical processing of psychodiagnostic results.
6. Interpretation of the results of mathematical processing.
7. Formulation of conclusions.

Empirical Research Hypothesis, as a rule, coincides with the hypothesis of the entire work and reflects the assumption about the relationship of indicators or their differences. There may be several hypotheses if the study uses many psychological indicators. Sometimes it is appropriate to formulate a general hypothesis and then specify it in several specific ones. For example:

General hypothesis: there are differences in motivation among organizational employees of different genders.

Particular hypotheses: 1) men are distinguished by a greater degree of motivation to achieve success; 2) women are distinguished by a greater expression of motivation for approval.

Sample of empirical research- these are the subjects or respondents who will participate in testing. When forming a sample, it is important that all subjects have similar socio-demographic characteristics. The work usually indicates the gender, age, and education of the respondents. If necessary, you can indicate your marital status and professional experience. The choice of characteristics is determined by the purpose and objectives of the study. For example, if personal factors of professional burnout in teachers are being studied, then it is hardly necessary to indicate the number of children when describing the sample.

Methods of empirical research- these are the tools that a psychologist uses to obtain empirical data about the psychological characteristics of subjects. There are the following types of techniques used in graduate research in psychology:

1. Questionnaires. This type of technique involves interviewing subjects about their socio-demographic characteristics, as well as some psychological characteristics. Questionnaires are not strictly reliable and valid psychological instruments. Therefore, their data is for reference and auxiliary purposes.
2. Questionnaires and tests are psychological tools standardized according to certain rules. With their help, you can obtain data about the psychological characteristics of the subjects. This data is considered valid and reliable, that is, reliable. This type of empirical research methods is most often used in coursework, diploma and master's degrees in psychology.
3. Projective techniques also make it possible to obtain data on the psychological characteristics of subjects, like questionnaires, but they are less standardized. Projective tests are rarely used in higher education tests in psychology, since their results are difficult to translate into numerical indicators. Projective techniques are more appropriate in clinical and psychotherapeutic practice for individual work.

The next important element of empirical research is the results of empirical research and their analysis. Considering its importance, let us dwell on it in more detail.

Results of empirical research and their analysis

The meaning of empirical research in psychology is to obtain results and, after analyzing them, formulate a conclusion about certain psychological patterns.

There are several types of empirical research results, reflecting the successive stages of their processing.

1. The first type of empirical research results are test results. The test subjects' responses to psychological questionnaires are processed using keys and entered into a summary table of results (it is usually placed in the appendix).
2. The second type of empirical research results are the results of statistical data processing. For example, a summary table of psychodiagnostic results is entered into a statistical program (for example, STATISTICA or SPSS) and correlations are calculated or differences are analyzed. These results are presented in the text of the work and are accompanied by a description and interpretation.

Typically, the analysis of the results of an empirical study is carried out in two stages:

1. The first stage is a qualitative analysis of data obtained from all psychodiagnostic methods. It involves constructing histograms or tables with distributions of indicators, as well as diagrams of average values.
2. The second stage is statistical data analysis. This stage involves presenting the results of statistical calculations in the form of tables. Below the tables is a description of the results and their interpretation.

Let us consider, as an example, the analysis of the results of an empirical study, the purpose of which was a comparative analysis of the coping strategies of young people from Russia and the USA.

Let only one technique be used - the Questionnaire “Methods of Coping Behavior” by R. Lazarus and S. Folkman (adapted by T.L. Kryukov, E.V. Kuftyak, M.S. Zamyshlyaev).

The sample included two groups of subjects: Group 1. Young people, citizens of Russia, 60 people (30 boys and 30 girls), age - from 20 to 25 years; live in Moscow; Group 2. Young people, US citizens, 60 people (30 boys and 30 girls), age - from 20 to 25 years; live in New York.

At the stage of qualitative analysis, we compare the structure of coping strategies in groups, presenting them in the form of a graph.

In Fig. Figure 1 shows the structures of coping strategies of young people from Russia and the USA.

Analysis of the data shown in Fig. 1 shows that in the group of subjects from Russia, coping strategies such as seeking social support and distancing are most pronounced. The least pronounced are flight-avoidance and self-control.

In the group of subjects from the USA, coping strategies such as planning to solve a problem and taking responsibility were most pronounced. The least pronounced are flight-avoidance and confrontational coping.

It is possible to note some common features of the structure of coping strategies in groups of subjects. Young people from Russia and the United States have the least pronounced escape-avoidance coping, that is, regardless of citizenship, young residents of megacities are not inclined to overcome negative experiences due to difficulties by reacting by the type of evasion: denying the problem, fantasizing, unjustified expectations, distraction and so on. This result may reflect the specifics of life in a metropolis, where infantile forms of behavior in the home life do not allow one to achieve success.

One can also note equally low values ​​for confrontational coping, which means that young people from Russia and the United States are equally not inclined to resolve problems through conflict behavior and outburst of emotions.

At the second stage of analyzing the results of the empirical study, we conduct a statistical analysis of the data using the Mann-Whitney U test, which allows us to identify statistically significant differences in the severity of coping strategies in the two groups.

The results of calculating significant differences in the indicators of coping strategies of young people from Russia and the USA are shown in Table 1.

Table 1. Results of calculating statistically significant differences in coping strategies and resilience of young people from Russia and the USA.

* - differences are statistically significant (p≤0.05)

Analysis of the data presented in Table 1 allows us to draw the following conclusions:

The level of the “distancing” coping strategy is statistically significantly higher in the group of young people from Russia. This means that, compared to Americans, Russian subjects tend to overcome difficult life situations by subjectively reducing its significance and the degree of emotional involvement in it; they are more characterized by the use of intellectual techniques of rationalization, switching attention, detachment, humor, devaluation, etc.

The level of the coping strategy “seeking social support” is statistically significantly higher in the group of young people from Russia. This means that, compared to Americans, Russian subjects tend to resolve problems by attracting external (social) resources, seeking informational, emotional and effective support; They are characterized by a focus on interaction with other people, an expectation of support, attention, advice, sympathy, and specific effective help.

The level of the “self-control” coping strategy is statistically significantly higher in the group of young people from the USA. This means that, compared to Russians, American subjects tend to overcome difficult life situations by purposefully suppressing and restraining emotions, minimizing their influence on the perception of the situation and the choice of behavior strategy with high behavioral control and the desire for self-control.

The level of the coping strategy “planning to solve a problem” is statistically significantly higher in the group of young people from the USA. This means that compared to Russians, American subjects tend to overcome difficult life situations through a targeted analysis of the situation and possible options for behavior, developing a strategy for resolving the problem, planning their own actions taking into account objective conditions, past experience and available resources.

It can be noted that there were no statistically significant differences in vitality indicators in groups of young people from Russia and the USA. This means that despite the differences in the ways of coping with stress and TJS, the measure of the ability of young people from Russia and the United States to withstand a stressful situation, maintaining internal balance and without reducing the success of their activities does not differ.

So, the analysis made it possible to identify national characteristics of coping with TJS among young Russians and Americans.

Young people from Russia in difficult life situations tend to distance themselves from the situation and thereby reduce its significance for themselves, and this shows a certain contemplativeness of the Russian mentality. It is also shown that young people from Moscow, to a greater extent than their peers from New York, tend to resort to social support in THS, which can be seen as a reflection of collectivist tendencies in the Russian character as opposed to individualistic ones in the American character.

Young Americans, to a greater extent than their Russian peers, tend to show self-control and control their behavior in TJS, which reflects the American national trait of emotional restraint. Also, young people from the United States, unlike their Russian peers, are more inclined to plan solutions to problems, which reflects the tendency of Americans in general to be focused on success, which involves planning activities.

1. Brief description of the specific result of statistical processing. For example, “The level of the coping strategy “distancing” is statistically significantly higher in the group of young people from Russia.”
2. Extended description of the result of statistical processing. For example, “This means that compared to Americans, Russian subjects tend to overcome difficult life situations by subjectively reducing its significance and the degree of emotional involvement in it; they are more characterized by the use of intellectual techniques of rationalization, switching attention, detachment, humor, devaluation, etc.”
3. Interpretation of the result of statistical processing. For example, “The identified differences in the use of the “distancing” coping strategy, from our point of view, are associated with differences in the Russian and American mentality. In particular, with more active Americans in foreign affairs and more contemplative Russians.”
4. General conclusion based on the results of the analysis of statistical data: “So, the analysis made it possible to identify national characteristics of coping with TJS among young Russians and Americans.
5. Young people from Russia in difficult life situations tend to distance themselves from the situation and thereby reduce its significance for... (see above)"

Types of empirical research in graduate research in psychology

Most often, in coursework, diploma or master's theses in psychology, within the framework of empirical research, it is supposed to state certain psychological patterns. That is, to identify what exists and this type of research is called ascertaining.

For example, in the example above we see a pattern ascertaining research- the researcher reveals differences in coping strategies among students from the USA and Russia and does not influence the situation in any way.

However, in some cases, psychologists do not limit themselves to making statements, but want to somehow correct or improve the situation.

For example, a psychologist conducts a comparative analysis of anxiety in boys and girls of senior preschool age. He receives some data, for example, that in the group of boys the number of children with very high levels of anxiety is statistically significantly higher than in the group of girls.

We can, of course, limit ourselves to stating this fact. However, most often the task is to correct anxiety in children. This problem is solved within the framework formative research.

Thus, the goal of formative research is the correction (reduction) of any unfavorable psychological quality that is overly expressed in the subjects. This could be anxiety, aggressiveness, a tendency to deviate behavior, etc.

The purpose of formative research may also be the development of some positive psychological quality that is not sufficiently developed in the subjects. These could be, for example, self-actualization, self-attitude, self-confidence, etc.

The forms of implementation of a formative experiment can be various kinds of corrective or developmental programs, psychological trainings, etc.

And finally, the third type of empirical research in final qualifying works in psychology is control study. Its purpose is to check how effective the program for correction or development of any psychological quality turned out to be.

As a rule, as part of formative empirical research, subjects are re-tested using the methods that were used in conducting the ascertaining research.

If the indicators have improved, for example, the aggressiveness of adolescents has decreased or the stress resistance of employees has increased, then the program or training is considered effective.

In coursework in psychology, only ascertaining studies are carried out.

In bachelor's theses and dissertations in psychology, ascertaining variants of empirical research are most often found, but it is also possible to use formative and control research.

In master's theses in psychology, quite often there are topics that involve conducting formative and control empirical research.

In 2013, we called our study “CASCO is getting cheaper.”

Unfortunately, today it seems like a bright dream. Over the past 18 months, CASCO prices have risen by 35%, and this, alas, is not the limit. In the third quarter of 2014, the price acceleration is only accelerating.

If the dynamics in the 1st quarter of 2014 relative to the 1st quarter of 2013 was +16%, then over the last six months the price increase was still the same.

What is the reason for such a rise in prices, especially after stable prices in recent years? All the blame lies with the very delayed adoption of the new law on compulsory motor liability insurance, which was finally adopted in July 2014, but, unfortunately, irreparable harm to the CASCO market has already been done.

Also adding fuel to the fire of the situation was the decision of the Supreme Court of the Russian Federation, which extended the law “On the Protection of Consumer Rights” to all types of auto insurance, and several very controversial decisions made by it in the courts.

All this ultimately fell on the shoulders of conscientious CASCO buyers, who in some cases felt a double increase in prices in their pockets.

We must note that over the past 18 months, we, as partners of insurance companies, have received a number of tariff increases, tightening of insurance rules, and in some regions - for certain car brands/models - even a complete ban on the sale of CASCO policies.

Among the insurance companies, the least expensive companies (as a percentage of the cost of the car) were Soglasie, Uralsib and Alliance (ROSNO), with prices increasing by up to 30%. And in such leading companies as Ingosstrakh, AlfaStrakhovanie and Rosgosstrakh, prices have increased by more than 40%!

This table shows price dynamics in Russian cities in 2014 compared to 2013.

If in most of the largest cities the average price increase was 10%, then in cities such as Vladivostok, Sochi and Ulyanovsk the price increase was 50% or more.

There are quite a lot of discussions in the government about stimulating the car market, but few people remember that it was the untimely adopted law on compulsory motor liability insurance that became one of the catalysts for the collapse in the car loan market, which, according to the latest data, fell by 50%. A mandatory condition when purchasing a car on credit is CASCO insurance. And CASCO costs amount to 20-30% of the total loan load for 2-3 year loans, even for experienced drivers. And for young people it’s 30-50%. The increase in CASCO prices, therefore, is another reason for the decline in the automobile market.

One of the country's leading insurers has introduced an additional surcharge of 15%, only for the fact that the insured car is a credit car and is insured without a deductible. Such a premium for CASCO insurance of a credit car is already an almost universal practice, thereby making a car loan even more unattractive for the buyer.

We examined the practice of using a franchise for CASCO insurance (which gives savings in the CASCO price of 20-40%) from 30 leading banks. More than half of these banks have a direct ban on the CASCO franchise when issuing a car loan, which increases the cost of CASCO for a car loan relative to the franchise up to 50%! And only 9 out of 30 banks allow the use of franchises within more or less comfortable limits.

Moneymatika always recommends CASCO insurance with a franchise to its clients, since along with 20-30% savings, the franchise allows you not to contact the insurance company for minor losses, thereby saving your time and improving the client’s insurance history and, as a result, makes it possible to get more favorable conditions for purchasing CASCO insurance for the next year.

We also see that insurance companies are also beginning to require the mandatory use of deductibles for the riskiest sections of clients (by age and by unprofitability of car brands/models). And the reluctance of banks to meet the client halfway in this matter surprises us all the more. We remind you that in most European countries, the use of a franchise is almost a mandatory condition for CASCO insurance!

As a result of rising prices, sales volumes in the insurance market begin to fall. In an effort to meet the needs of the client, while maintaining the economics of the business, insurance companies are increasingly beginning to offer a new type of CASCO - economical CASCO! The essence of the product is that when purchasing CASCO insurance, the client pays only the first 50-55% of the full cost of the policy, and the rest is paid in the form of deductible payments only when an insured event occurs. It turns out that if during the insurance period (usually 1 year) an insured event does not occur, the client saves up to 50% of funds. Examples of such products are AlfaStrakhovanie “CASCO 50x50+” and Rosgosstrakh “Economy” package. We recommend these products.

CASCO for a young driver under 25 years old is more than 2 times more expensive than CASCO for an experienced driver over 40 years of age! And the maximum increase in prices for the year – 20% – fell precisely on the category of the youngest drivers. For CASCO insurance, they often have to pay six-figure sums in rubles.

At the same time, the price increase for experienced drivers over the age of 30 turned out to be the least sensitive - only 6-8%, which is several times less than the average dynamics for the year.

There is an opinion that the most expensive CASCO for a car will be in the first year of its insurance. In subsequent years, the car becomes cheaper, and you will need to pay less for CASCO. This is not an entirely correct judgment - insurers are gradually increasing CASCO rates for aging cars and, according to statistics, in the first 5 years CASCO for a given car will cost approximately the same amount, even though during this time the car loses 30-60 % of its value.

But after 5 years of age, car insurance becomes a very expensive pleasure. Despite the low residual value of the car, the absolute price of CASCO begins to literally take off, and for 8-9 years of insurance it will be 20% of the cost of the car, which is 3 times more expensive than insurance for a new car as a % of the cost of the car! Insurance companies still cannot offer interesting insurance options for such cars. What is offered is subject to a large number of conditions, which is why it is not very attractive. And almost no company will insure cars older than 10 years.

You are doubly unlucky if you find your car model in this table. Here are the 30 most expensive car brands/models among the 200 most popular. Thus, the owner of a Lexus GS car will have to fork out 150,000-200,000 rubles when purchasing CASCO insurance, which will be 50% more expensive than last year!

In our practice, there are already quite a lot of cases when clients almost lose consciousness or begin to be loudly indignant upon learning that the price of renewing insurance, even with a break-even ride, turns out to be twice as high as last year.

In this table we have shown the dynamics of CASCO prices for the 30 most popular brands/models of cars. The table compares average prices in 2014 relative to average prices in 2013. But keep in mind, as we said at the very beginning of the study, prices in Q3 2014 are 30% higher than prices 18 months ago.