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Stochastic programs without duality gaps

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  • Teemu Pennanen
  • Ari-Pekka Perkkio

Abstract

This paper studies dynamic stochastic optimization problems parametrized by a random variable. Such problems arise in many applications in operations research and mathematical finance. We give sufficient conditions for the existence of solutions and the absence of a duality gap. Our proof uses extended dynamic programming equations, whose validity is established under new relaxed conditions that generalize certain no-arbitrage conditions from mathematical finance.

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  • Teemu Pennanen & Ari-Pekka Perkkio, 2011. "Stochastic programs without duality gaps," Papers 1105.0934, arXiv.org.
    • Handle: RePEc:arx:papers:1105.0934
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    References listed on IDEAS

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    1. I. V. Evstigneev, 1976. "Measurable Selection and Dynamic Programming," Mathematics of Operations Research, INFORMS, vol. 1(3), pages 267-272, August.
    2. Bertsekas, Dimitri P., 1974. "Necessary and sufficient conditions for existence of an optimal portfolio," Journal of Economic Theory, Elsevier, vol. 8(2), pages 235-247, June.
    3. Teemu Pennanen, 2011. "Arbitrage and deflators in illiquid markets," Finance and Stochastics, Springer, vol. 15(1), pages 57-83, January.
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