A stochastic quantization method for nonlinear problems

TitleA stochastic quantization method for nonlinear problems
Publication TypeJournal Article
Year of Publication2001
AuthorsVlad Bally, Gilles Pagès, and Jacques Printems
JournalMonte Carlo Methods and Applications
Keywordsalgorithm, American exchange options, American option pricing, error bounds, free boundary, numerical examples, Optimal Stopping, quantization, Reflected Backward Stochastic Differential Equation, Snell envelope

We give an algorithm based on the quantization method which computes the solution of multi-dimensional obstacle problems, e.g. the pricing of American option on a basket of assets. More generally this algorithm applies to semi-linear partial differential equations with free boundary, or, in probabilistic terms, to reflected backward stochastic differential equations. Some a priori estimates of the error are obtained. A numerical illustration about the pricing of American exchange options is proposed.