| Title | A stochastic quantization method for nonlinear problems |
| Publication Type | Journal Article |
| Year of Publication | 2001 |
| Authors | Vlad Bally, Gilles Pagès, and Jacques Printems |
| Journal | Monte Carlo Methods and Applications |
| Volume | 7(1) |
| Pagination | 21-34 |
| Keywords | algorithm, American exchange options, American option pricing, error bounds, free boundary, numerical examples, Optimal Stopping, quantization, Reflected Backward Stochastic Differential Equation, Snell envelope |
| Abstract | 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. |
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