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The Monotone Case Approach for the Solution of Certain Multidimensional Optimal Stopping Problems
Sören Christensen, Albrecht Irle · 2017-05-04 · via math.PR updates on arXiv.org

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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