Abstract
As catastrophic events happen more and more frequently, accurately forecasting risk at a high level is vital for the financial stability of the insurance industry. This paper proposes an efficient three-step procedure to deal with the semicontinuous property of insurance claim data and forecast extreme risk. The first step uses a logistic regression model to estimate the nonzero claim probability. The second step employs a quantile regression model to select a dynamic threshold for fitting the loss distribution semiparametrically. The third step fits a generalized Pareto distribution to exceedances over the selected dynamic threshold. Combining these three steps leads to an efficient risk forecast. Furthermore, a random weighted bootstrap method is employed to quantify the uncertainty of the derived risk forecast. Finally, we apply the proposed method to an automobile insurance data set.