On the Approximation of Optimal Stopping Problems with Application to Financial Mathematics

Abstract

The determination of the value function associated with a given reward and stochastic process represents an important class of stochastic control problem. In particular, the expectations of such processes may be represented as solutions of variational inequalities of evolutionary type typically characterized by their high number of degrees of freedom, unbounded domains, and lack of "natural" boundary conditions. In this paper, we introduce two methodologies for computing the value function of optimal stopping associated with general stochastic processes. Our results are implemented utilizing finite elements and are validated using problems taken from financial mathematics.

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