RBF And Optimal Stopping Problems: AnApplication To The Pricing Of Vanilla Options OnOne Risky Asset

Abstract

The determination of the optimal stopping frontier associated with a given reward function and stochastic process represents an important class of stochastic control problem. In particular, the expectations of such problems may be represented as solutions of variational inequalities of evolutionary type and are typically characterized by their associated high number of degrees of freedom, unbounded domains, and lack of boundary conditions. In this paper, we utilize Radial Basis Functions (RBF) to approximate the solution of a class of optimal stopping problems from financial mathematics; the pricing of vanilla options written on a single risky asset. We investigate the influence of the computational domain, domain decomposition and mesh scaling on the computed solution.