Importance Sampling for Backward SDEs

In this article, we explain how the importance sampling technique can be generalized from simulating expectations to computing the initial value of backward stochastic differential equations (SDEs) with Lipschitz continuous driver. By means of a measure transformation we introduce a variance reduced...

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Bibliographic Details
Published in:Stochastic analysis and applications 2010-02, Vol.28 (2), p.226-253
Main Authors: Bender, Christian, Moseler, Thilo
Format: Article
Language:English
Subjects:
Algorithms
BSDE
Computer simulation
Differential equations
Distribution theory
Exact sciences and technology
Importance sampling
Linear inference, regression
Mathematics
Monte Carlo methods
Monte Carlo simulation
Numerics
Pricing
Probability and statistics
Probability theory and stochastic processes
Sciences and techniques of general use
Statistics
Stochastic analysis
Stochastic processes
Stochasticity
Transformations
Variance reduction
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Summary:In this article, we explain how the importance sampling technique can be generalized from simulating expectations to computing the initial value of backward stochastic differential equations (SDEs) with Lipschitz continuous driver. By means of a measure transformation we introduce a variance reduced version of the forward approximation scheme by Bender and Denk [ 4 ] for simulating backward SDEs. A fully implementable algorithm using the least-squares Monte Carlo approach is developed and its convergence is proved. The success of the generalized importance sampling is illustrated by numerical examples in the context of Asian option pricing under different interest rates for borrowing and lending.
ISSN:0736-2994
1532-9356
DOI:10.1080/07362990903546405