Riesz representation and optimal stopping with two case studies

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Publication Details

List of Authors: Sören Christensen, Paavo Salminen
Publisher: Corenell University Library, arXiv.org > math > arXiv:1309.2469v2
Publication year: 2014


Abstract

In this paper we demonstrate that optimal stopping problems can be studied very effectively using as the main tool the Riesz integral representation of excessive functions. After a short general discussion of the Riesz representation we concretize, firstly, on a d-dimensional and, secondly, a space-time one-dimensional geometric Brownian motion. After this, two classical optimal stopping problems are discussed: 1) the optimal investment problem and 2) the valuation of the American put option. It is seen in both of these problems that the boundary of the stopping region can be characterized as a unique solution of an integral equation arising immediately from the Riesz representation of the value function. In Problem 2 the derived equation coincides with the standard well-known equation found in the literature.

Last updated on 2020-26-02 at 07:00