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A provisioning problem with stochastic payments

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Listed author(s):
  • Pagnoncelli, Bernardo K.
  • Vanduffel, Steven

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 find 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 efficient 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.

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File URL: http://www.sciencedirect.com/science/article/pii/S0377221712002469
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Article provided by Elsevier in its journal European Journal of Operational Research.

Volume (Year): 221 (2012)
Issue (Month): 2 ()
Pages: 445-453

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Handle: RePEc:eee:ejores:v:221:y:2012:i:2:p:445-453
DOI: 10.1016/j.ejor.2012.01.065
Contact details of provider: Web page: http://www.elsevier.com/locate/eor

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

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  1. Dilip B. Madan & Frank Milne, 1991. "Option Pricing With V. G. Martingale Components," Mathematical Finance, Wiley Blackwell, vol. 1(4), pages 39-55.
  2. Dupacova, Jitka & Gaivoronski, Alexei & Kos, Zdenek & Szantai, Tamas, 1991. "Stochastic programming in water management: A case study and a comparison of solution techniques," European Journal of Operational Research, Elsevier, vol. 52(1), pages 28-44, May.
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  7. Cesari, Riccardo & Cremonini, David, 2003. "Benchmarking, portfolio insurance and technical analysis: a Monte Carlo comparison of dynamic strategies of asset allocation," Journal of Economic Dynamics and Control, Elsevier, vol. 27(6), pages 987-1011, April.
  8. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
  9. Vanduffel, Steven & Shang, Zhaoning & Henrard, Luc & Dhaene, Jan & Valdez, Emiliano A., 2008. "Analytic bounds and approximations for annuities and Asian options," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1109-1117, June.
  10. Vanduffel, S. & Dhaene, J. & Goovaerts, M. & Kaas, R., 2003. "The hurdle-race problem," Insurance: Mathematics and Economics, Elsevier, vol. 33(2), pages 405-413, October.
  11. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters,in: THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78 World Scientific Publishing Co. Pte. Ltd..
  12. Abdelaziz, Fouad Ben & Aouni, Belaid & Fayedh, Rimeh El, 2007. "Multi-objective stochastic programming for portfolio selection," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1811-1823, March.
  13. Kampas, Athanasios & White, Ben, 2003. "Probabilistic programming for nitrate pollution control: Comparing different probabilistic constraint approximations," European Journal of Operational Research, Elsevier, vol. 147(1), pages 217-228, May.
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Cited by:

  1. Tsai, Shing Chih & Zheng, Ya-Xin, 2013. "A simulation optimization approach for a two-echelon inventory system with service level constraints," European Journal of Operational Research, Elsevier, vol. 229(2), pages 364-374.

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