Sample-path solution of stochastic variational inequalities, with applications to option pricing

Abstract

This paper shows how to apply a variant of sample-path optimization to solve stochastic variational inequalities, including as a special case finding a zero of a gradient. We give a new set of sufficient conditions for almost-sure convergence of the method, and exhibit bounds on the error of the resulting approximate solution. We also illustrate the application of this method by using it to price an American call option on a dividend-paying stock.