Snell Envelope with Small Probability Criteria

Snell Envelope with Small Probability Criteria We present a new algorithm to compute the Snell envelope in the specific case where the criteria to optimize is associated with a small probability or a rare event. This new approach combines the Stochastic Mesh approach of Broadie and Glasserman with a particle approximation scheme based on a specific change of measure designed to concentrate the computational effort in regions pointed out by the criteria. The theoretical analysis of this new algorithm provides non asymptotic convergence estimates. Finally, the numerical tests confirm the practical interest of this approach. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Snell Envelope with Small Probability Criteria

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Publisher
Springer-Verlag
Copyright
Copyright © 2012 by Springer Science+Business Media New York
Subject
Mathematics; Mathematical Methods in Physics; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization; Numerical and Computational Physics; Theoretical, Mathematical and Computational Physics
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-012-9173-1
Publisher site
See Article on Publisher Site

Abstract

We present a new algorithm to compute the Snell envelope in the specific case where the criteria to optimize is associated with a small probability or a rare event. This new approach combines the Stochastic Mesh approach of Broadie and Glasserman with a particle approximation scheme based on a specific change of measure designed to concentrate the computational effort in regions pointed out by the criteria. The theoretical analysis of this new algorithm provides non asymptotic convergence estimates. Finally, the numerical tests confirm the practical interest of this approach.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Dec 1, 2012

References

  • Interacting particle systems for the computation of rare credit portfolio losses
    Carmona, R.; Fouque, J.-P.; Vestal, D.

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