A Provisioning Problem with Stochastic Payments

Abstract

We consider the problem of determining the minimal requirement one must establish in order to meet a series of future random payments. It is shown in a very general setting that this problem can be recast as a chance constrained model and how the technique of Sample Average Approximation can be employed to find solutions. We also use comonotonic theory to analyze analytical approximations in a restricted Gaussian setting. Our numerical illustrations demonstrate that the Sample Average Approximation is a viable and effcient way to solve the stated problem generally and outperforms the analytical approximations. In passing we present a result that is related to Stein's famous lemma (Stein, 1981) and is of interest in itself.

Keywords: Risk management, Solvency, Comonotonicity, Sample Average Approximation