The Research Of The Method Of Application Of Extreme Value Theory In Non-life Insurance

Based on the extreme value theory, this thesis introduced how the theory and the extreme value model be used in the risk measuring. This thesis also systematically expounds how the theory is used in the insurance in details and creatively uses the model to measure the general capital reserve. From the angle of risk-analysis, it creates a more accurate approach of measuring the general capital reserve.Before risk management, risk should be accurately measured. There are several means, most commonly used are:variance and standard deviation, probability of going bankrupt, value at risk and the risk-measuring which based on varying functions. Comparing the advantages and disadvantages of various kinds of measuring approaches and combining the characteristics of thick tail which presents by the data of the non-life insurance, we chose high quantiles or value at risk as the risk-measuring approach.Because the non-life insurance always demonstrates thick tail of compensation, this thesis has draw into the hazard rate and mean excess loss to judge and examine the tail of the theory-distribution. What's more, diagrammatizing tool which include index QQ diagram, empirical mean excess loss has been used to diagnose and examine the thick tail of the data.Extreme value theory can be divided into two types of model while measuring risk. One is block maxima model which mainly model the maximum value for group data. The other, in the generalized way, is called Pareto model, abbreviated as GPD model or POT model. It models the data which surpass a comparative high threshold value under observation. Because of the limited utilization rate and limited extreme observation data, the GPD model frequently adopt in practical. This thesis introduces the fundamental theory of the distribution of extreme value. In the explanation of the extreme value theorem, it extracts the distribution of Frechet, Gumbel and Weibull, offers the forms and field of definitions and finally unifies the three distributions in generalized extreme value. While estimating the parameter of the distribution of the generalized extreme value, the maximum likelihood estimation and probability-weighted moments are the effective and commonly used means. Based on the distribution of the generalized extreme value, the author obtains the formula of BMM model to measuring risks. So long as make use of data to work out the parameter of the BMM model, the estimated value of risk can be obtained. For the GPD model, the author abides by the same approach, introducing the model itself and the estimation of the parameter, and finally working out the expression of the GPD model for risk-measuring.Due to risk management or risk scatter, non-life insurance companies always need reinsurance. Then, how to accurately transform the risk or pricing the reinsurance turns to be an essential item that non-life insurance company and reinsurance company should concern.Because the non-life insurance presents the characteristic of thick tail, homogeneous distribution makes the accurate fitting of compensation data very difficult, especially for the fitting of thick tail.However, the commonly used practical means of reinsurance pricing, includes risk-pricing, rate-on-line or payback and pure loss cost has the weaknesses as follow:Firstly, the data of compensation is insufficient or the volatility of data is huge, which will lead to the increase of the derivation of reinsurance pricing, so that the operation of the insurance company will be influenced. Secondly, owing to lack of the data of extreme value compensation, how to reasonably take extreme value into account in pricing should be resolved.Therefore, it is possible that these means are not suitable for the reinsurance pricing for non-life insurance business which presents thick tail compensation data.For insurance company or reinsurance company, both of them need to effectively manage and take precautions against the natural disaster or extreme value risk. Occurrence of extreme value risk will cause the deviation of compensation of insurance business from the normal expectation, influence the experience of insurance and probably lead to the deficit or even bankrupt. Therefore, frequently, insurance need extract general capital reserve to cope with the extreme value risk. Catastrophe reserves or general capital reserve is a reserve which responds to unexpected loss and according to the loss accounts and draws. The accounting and drawing of the catastrophe reserves is of importance, so accurate calculation of the amount of reserve is necessary. In the advanced countries, while confirming and measuring the catastrophe reserve, insurance companies generally comply with the fixed formula in law or rule. However, in our country, there is not a definite provision for the means of accounting and drawing of general capital reserve. It just set to extract particular proportion from the profit, but not a definite number of proportion. Even though the confirmation and measurement in abroad is according to the fixed formula in law or provision, its rationality still needs to be proved. There is not a mean of calculation suitable for the entire situation. Extreme value theory can accurately measure the thick tail risk. According to high quantiles, by means of the typical value of sample and the probability of the occurrence of the extreme value events, the general capital reserve can be estimated.In the end, this thesis, by means of the empirical results of the scholar's research findings and data, reveals the application of extreme value theory in risk-measuring, pricing of reinsurance and general capital reserve of by the form of an example.