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A provisioning problem with stochastic payments

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  • 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.

Suggested Citation

  • Pagnoncelli, Bernardo K. & Vanduffel, Steven, 2012. "A provisioning problem with stochastic payments," European Journal of Operational Research, Elsevier, vol. 221(2), pages 445-453.
  • Handle: RePEc:eee:ejores:v:221:y:2012:i:2:p:445-453
    DOI: 10.1016/j.ejor.2012.01.065
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    1. 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.
    2. Dilip B. Madan & Frank Milne, 1991. "Option Pricing With V. G. Martingale Components1," Mathematical Finance, Wiley Blackwell, vol. 1(4), pages 39-55, October.
    3. 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.
    4. 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.
    5. Dilip B. Madan & Frank Milne, 1991. "Option Pricing With V. G. Martingale Components," Working Paper 1159, Economics Department, Queen's University.
    6. 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.
    7. Kaas, Rob & Dhaene, Jan & Goovaerts, Marc J., 2000. "Upper and lower bounds for sums of random variables," Insurance: Mathematics and Economics, Elsevier, vol. 27(2), pages 151-168, October.
    8. J. Dhaene & S. Vanduffel & M. J. Goovaerts & R. Kaas & D. Vyncke, 2005. "Comonotonic Approximations for Optimal Portfolio Selection Problems," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 72(2), pages 253-300, June.
    9. A. Charnes & W. W. Cooper & G. H. Symonds, 1958. "Cost Horizons and Certainty Equivalents: An Approach to Stochastic Programming of Heating Oil," Management Science, INFORMS, vol. 4(3), pages 235-263, April.
    10. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    11. 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.
    12. Hürlimann, Werner, 2010. "Analytical Pricing of the Unit-Linked Endowment with Guarantees and Periodic Premiums," ASTIN Bulletin, Cambridge University Press, vol. 40(2), pages 631-653, November.
    13. 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.
    14. 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. Carole Bernard & Ludger Rüschendorf & Steven Vanduffel, 2017. "Value-at-Risk Bounds With Variance Constraints," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 84(3), pages 923-959, September.
    2. 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.
    3. Xu, Liang & Gao, Chunyan & Kou, Gang & Liu, Qinjun, 2017. "Comonotonic approximation to periodic investment problems under stochastic drift," European Journal of Operational Research, Elsevier, vol. 262(1), pages 251-261.

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