Functional sensitivity analysis of ruin probability in the classical risk models

Abstract

Sensitivity analysis investigates how the change in the output of a computational model can be attributed to changes of its input parameters. Identifying the input parameters that propagate more uncertainty on the ruin probability associated with insurance risk models is a challenging problem. In this paper, we consider the classical risk model, where an epistemic-uncertainty veils the true values of the claim size distribution rate and the Poisson arrival rate. Based on the available data for calibrating the probability distributions that model gaps of knowledge on these rates, and using the Taylor-series expansion methodology, we obtain the ruin probability under polynomial form in uncertain rates as a computational model. Specifically, we get a new sensitivity estimate of the ruin probability with respect to uncertain parameters. We provide a coherent framework within which we can accurately characterize statistically the uncertain ruin probability. In addition, we use the Markov's inequality to estimate the risk incurred by working with uncertain ruin probability rather than that evaluated at fixed parameters. A series of numerical experiments are presented to illustrate the potential of the proposed approach.