On optimal stopping of multidimensional diffusions

D4 Published development or research report or study

Internal Authors/Editors

Publication Details

List of Authors: Sören Christensen, Fabian Crocce, Ernesto Mordecki, Paavo Salminen
Publisher: ArXiv.org
Publication year: 2016
Start page: 1
End page: 19


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 derive 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. It turns out that these integral equations have many advantages over alternative equations.
These equations allow to formulate a discretization scheme to obtain an approximate solution.
The approach is illustrated through the optimal stopping problem of a $d$-dimensional Wiener process
with a positive definite quadratic form reward function.

Last updated on 2020-07-07 at 04:41