Estimating a VaR-type ruin measure by Laguerre series expansion in classical compound Poisson risk model

Abstract

Value at Risk (VaR) has been extensively applied within the banking and financial sectors. Regulators use it to reflect riskiness and determine capital requirements. In this paper, we propose an efficient method for estimating a VaR-type ruin measure under the classical risk model. We first use Laguerre series expansion to approximate the ruin probability and utilize a tabularization method to approximate the VaR-type ruin measure. A practical scenario where the distribution of individual claim size and the Poisson intensity are unknown has been considered. Based on observed data providing claim information, we illustrate the estimation of the VaR ruin measure. Moreover, the approximation convergence rates and statistical errors are studied, respectively. Various numerical examples are provided to demonstrate the performance of the proposed method.