On optimal stopping of multidimensional diffusions

D4 Publicerad utvecklings- eller forskningsrapport eller studie


Interna författare/redaktörer


Publikationens författare: Sören Christensen, Fabian Crocce, Ernesto Mordecki, Paavo Salminen
Förläggare: ArXiv.org
Publiceringsår: 2016
Artikelns första sida, sidnummer: 1
Artikelns sista sida, sidnummer: 19


Abstrakt

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.

Senast uppdaterad 2020-29-01 vid 03:02