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The monotone case approach for the solution of certain multidimensional optimal stopping problems

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  • Christensen, Sören
  • Irle, Albrecht

Abstract

This paper studies explicitly solvable multidimensional optimal stopping problems of sum- and product-type in discrete and continuous time using the monotone case approach. It gives a review on monotone case stopping using the Doob decomposition, resp. Doob–Meyer decomposition in continuous time, also in its multiplicative versions. The approach via these decompositions leads to explicit solutions for a variety of examples, including multidimensional versions of the house-selling and burglar’s problem, the Poisson disorder problem, and an optimal investment problem.

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  • Christensen, Sören & Irle, Albrecht, 2020. "The monotone case approach for the solution of certain multidimensional optimal stopping problems," Stochastic Processes and their Applications, Elsevier, vol. 130(4), pages 1972-1993.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:4:p:1972-1993
    DOI: 10.1016/j.spa.2019.06.009
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    Cited by:

    1. Soren Christensen & Albrecht Irle & Julian Peter Lemburg, 2021. "Flexible forward improvement iteration for infinite time horizon Markovian optimal stopping problems," Papers 2111.13443, arXiv.org.

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