On optimal stopping of multidimensional diffusions

Sören Christensen, Fabian Crocce, Ernesto Mordecki, Paavo Salminen

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    13 Citations (Scopus)


    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 associated with the problem. 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.

    Original languageUndefined/Unknown
    Pages (from-to)2561–2581
    JournalStochastic Processes and their Applications
    Issue number7
    Publication statusPublished - 2019
    MoE publication typeA1 Journal article-refereed

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