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Discretisation and duality of optimal Skorokhod embedding problems

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  • Cox, Alexander M.G.
  • Kinsley, Sam M.

Abstract

We prove a strong duality result for a linear programming problem which has the interpretation of being a discretised optimal Skorokhod embedding problem, and we recover this continuous time problem as a limit of the discrete problems. With the discrete setup we show that for a suitably chosen objective function, the optimiser takes the form of a hitting time for a random walk. In the limiting problem we then reprove the existence of the Root, Rost, and cave embedding solutions of the Skorokhod embedding problem.

Suggested Citation

  • Cox, Alexander M.G. & Kinsley, Sam M., 2019. "Discretisation and duality of optimal Skorokhod embedding problems," Stochastic Processes and their Applications, Elsevier, vol. 129(7), pages 2376-2405.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:7:p:2376-2405
    DOI: 10.1016/j.spa.2018.07.008
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    References listed on IDEAS

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    15. Alexander M. G. Cox & Sam M. Kinsley, 2017. "Robust Hedging of Options on a Leveraged Exchange Traded Fund," Papers 1702.07169, arXiv.org.
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