The Application Of Semiparametric Mixture Model In Extreme Value Under Bayesian Approach

Rare extreme events have characteristics of small probability and large loss, its accident can cause a lot of direct or indirect economic loss, threatening the stability of management of insurance company. Therefore, the prediction of rare extreme events is particularly important. At present, the prediction method that is widely used in rare extreme events is the extreme value theory, however, extreme value theory is extremely sensitive to the selection of threshold, and users' subjective judgment. Also, EVT could not evaluate the uncertainty of the parameters, unable to understand the parameters'statistical feature parameters and can't get the confidence interval of parameters. The bayesian method can solve those problems very well. Based on the extreme value theory, in semiparametric mixture model use semiparametric model to estimate the density of the data below the threshold and use generalized pareto distribution above the threshold.Generalized pareto distribution works well in the estimations of extreme quantile, especially in heavy tail distribution. This paper uses bayesian modeling method by choosing appropriate the prior distribution of parameters, combined with the likelihood function, deduce the mixed posterior distribution of the model, then using markov monte carlo (MCMC) sampling was carried out on the posterior distribution, then parameters is obtained by analyzing the results of the statistical characteristics.The semiparametric model was used when choosing the model below the threshold. Semiparametric model is numerical approximation method, the theory is relatively mature, and it is widely applicated in the world, but the existing research does not apply to the bayesian estimation, nor with the combination of extreme value theory. In this article semiparameter is introduced in the study of damage assessment model in order to achieve a more accurate prediction results. This model can effectively improve the current popular method of extreme value theory and parameter mixtyre model. The empirical results show that the semiparametric model below the threshold for part of the fitting effect is superior to the parametric model, finally the forecasting results of loss distribution is more reasonable, and it also forecast the quantiles of spike thick tail according to set provides a way to improve. Therefore, this paper improved the accuracy of the prediction of the extreme quantile, providing a new way of loss prediction.