On optimal stopping of multidimensional diffusions

Sören Christensen, Fabián Crocce, Ernesto Mordecki and Paavo Salminen

Stochastic Processes and their Applications, 2019, vol. 129, issue 7, 2561-2581

Abstract: This paper develops an approach for solving perpetual discounted optimal stopping problems for multidimensional diffusions, with special emphasis on the d-dimensional Wiener process. We first obtain some verification theorems for diffusions, based on the Green kernel representation of the value function. Specializing to the multidimensional Wiener process, we apply the Martin boundary theory to obtain a set of tractable integral equations involving only harmonic functions that characterize the stopping region of the problem in the bounded case. The approach is illustrated through the optimal stopping problem of a d-dimensional Wiener process with a positive definite quadratic form reward function.

Keywords: Optimal stopping; Multidimensional diffusions; Martin kernel; Green kernel; Helgason support theorem; Quadratic reward (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (9)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:129:y:2019:i:7:p:2561-2581

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DOI: 10.1016/j.spa.2018.07.014

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