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

Sören Christensen and Albrecht Irle

Stochastic Processes and their Applications, 2020, vol. 130, issue 4, 1972-1993

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.

Keywords: Monotone stopping rules; Optimal stopping; Doob–Meyer decomposition; Multiple buying–selling; Poisson disorder problem; Optimal investment problem (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.spa.2019.06.009

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