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A Provisioning Problem with Stochastic Payments

Final version in European Journal of Operational Research

30 Pages Posted: 9 Dec 2011 Last revised: 31 Jan 2012

Bernardo Pagnoncelli

University of Adolfo Ibanez - School of Business

Steven Vanduffel

Vrije Universiteit Brussel (VUB)

Date Written: December 7, 2011

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

Suggested Citation

Pagnoncelli, Bernardo and Vanduffel, Steven, A Provisioning Problem with Stochastic Payments (December 7, 2011). Final version in European Journal of Operational Research. Available at SSRN: https://ssrn.com/abstract=1969601 or http://dx.doi.org/10.2139/ssrn.1969601

Bernardo Pagnoncelli (Contact Author)

University of Adolfo Ibanez - School of Business ( email )

Santiago
Chile
56 2 2331 1155 (Phone)

Steven Vanduffel

Vrije Universiteit Brussel (VUB) ( email )

Pleinlaan 2
Brussels, Brabant 1050
Belgium

HOME PAGE: http://www.stevenvanduffel.com

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