Applying Generalized Pareto Distribution to the Risk Management of Commerce Fire Insurance

This paper focus on modeling and estimating tail parameters of commercial fire loss severity. Using extreme value theory, we centralized on the generalized Pareto distribution (GPD) and compare with standard parametric modeling based on Lognormal, Exponential, Gamma and Weibull distributions. In empirical study, we determine the thresholds of GPD through mean excess plot and Hill plot. Kolmogorv-Smirnov and LR goodness-of-fit test are conducted to assess how good the fit is. VaR and expected shortfall are also calculated. We also take into account bootstrap method to estimate the confidence interval of parameters. Empirical results show that the GPD method is a theoretically well supported technique for fitting a parametric distribution to the tail of an unknown underlying distribution. It can capture the tail behavior of commercial fire insurance loss very well.