Large Insurance Claims Data Statistical Analysis Of Extreme Value And Applications

Risk management is very important for insurance companies, the loss distribution model is a reasonable basis for the development of the premium and directly related to the quality of risk management. In the past, the exponential distribution, lognormal distribution, gamma distribution, have been used to fit the data of claims, but when large claims often occur,the tail of these distributions for fitting results become not very good. The loss is often underestimated. Since the occurrence of large claims could have a devastating impact on the insurance company, a certain method for proper fit for large claims is needed.Statistics analysis of extreme value are very useful in modeling rare event whose happen will have a huge impact, and its application has been deep into the hydrology, meteorology, finance, insurance and other fields.To overcome the above shortcomings, this paper discusses a statistical modeling strategy based on extreme value theory to describe the behavior of two insurance porfolios, with particular emphasis on large claims.The stratege is illustrated using the1991group medical claims database maintained by the Society of Actuaries and the1998-2009fire claims datas which happened in China. Using extreme value theory,the modeling strategy focuses on the "excesses over threshold" approach to fit generalized Pareto distributions.The proposed strategy is compared to standard parametric modeling based on gamma, loggamma, and lognormal distributions.Extreme value theory outperforms classical parametric fits and allows the actuary to easily estimate high quantiles,net premium,and initial reserve for reinsurance. Fitting the generalized Pareto distribution to large claims can overcome the previous underestimation of the insurance risk, which makes the insurance company to be more cautious, a reasonable estimation of insurance risk. It is of great significance to guide its risk management.