Tail-Related Risk Measures of Extreme Value Distribution: The Case of Taiwan’s Rice Damage Due to Typhoons in the Non-Crops Insurance Plan

This paper adopts the extreme value and VaR approach to investigate the amount of rice damaged due to extreme events and analyzes the collective risk model as a feasible scheme for estimating annual aggregate losses. The results show that the annual frequency of rice damage caused by typhoons is shown to fit well the Poisson distribution with one parameter. The generalized Pareto distribution (GPD) with two parameters outperforms the log-normal fit with respect to the tail-related risk measures, e.g., VaR, ES, and EAS. GPD allows easy estimation of the high quantiles and the maximum probable loss from the data. The threshold value can be used as reference in decision making for setting grant-in-cash relief. We believe that, given different confidence intervals, these high-quantile measures can provide useful information in reviewing the applicable loss compensation regulations and for adjusting natural disaster relief budget plans or insurance pricing on the non-insurance plan.