Discretisation and duality of optimal Skorokhod embedding problems

Alexander M.G. Cox and Sam M. Kinsley

Stochastic Processes and their Applications, 2019, vol. 129, issue 7, 2376-2405

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.

Date: 2019
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DOI: 10.1016/j.spa.2018.07.008

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