Riesz representation and optimal stopping with two case studies

Sören Christensen, Paavo Salminen

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    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.
    Original languageUndefined/Unknown
    PublisherCorenell University Library, arXiv.org > math > arXiv:1309.2469v2
    Publication statusPublished - 2014
    MoE publication typeD4 Published development or research report or study

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