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Stochastic programs without duality gaps


  • Teemu Pennanen
  • Ari-Pekka Perkkio


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,
  • Handle: RePEc:arx:papers:1105.0934

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    1. Damien Lamberton & Mohammed Mikou, 2008. "The critical price for the American put in an exponential Lévy model," Finance and Stochastics, Springer, vol. 12(4), pages 561-581, October.
    2. Guy Barles & Julien Burdeau & Marc Romano & Nicolas Samsoen, 1995. "Critical Stock Price Near Expiration," Mathematical Finance, Wiley Blackwell, vol. 5(2), pages 77-95.
    3. Peter Carr & Robert Jarrow & Ravi Myneni, 2008. "Alternative Characterizations Of American Put Options," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 5, pages 85-103 World Scientific Publishing Co. Pte. Ltd..
    4. S. D. Jacka, 1991. "Optimal Stopping and the American Put," Mathematical Finance, Wiley Blackwell, vol. 1(2), pages 1-14.
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