Articlegreen2010

Solving BSDE with Adaptive Control Variate

68 citations0/0 files storedSIAM Journal on Numerical Analysis

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Stochastic processes and financial applications Numerical methods for differential equations Fuzzy Systems and Optimization

Abstract

We present and analyze an algorithm to solve numerically BSDEs based on Picard's iterations and on a sequential control variate technique. Its convergence is geometric. Moreover, the solution provided by our algorithm is regular both w.r.t. time and space.

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References

2008Stochastic differential equations and applications 1997Backward Stochastic Differential Equations in Finance 1976Stochastic Differential Equations and Applications 2005Backward stochastic differential equations and quasilinear parabolic partial differential equations 1994Solving forward-backward stochastic differential equations explicitly — a four step scheme 1997Reflected solutions of backward SDE's, and related obstacle problems for PDE's 2004Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations 2005A regression-based Monte Carlo method to solve backward stochastic differential equations

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2020Overcoming the curse of dimensionality in the approximative pricing of financial derivatives with default risks 2010L2 -time regularity of BSDEs with irregular terminal functions 2013A Sparse-Grid Method for Multi-Dimensional Backward Stochastic Differential Equations 2016Stratified Regression Monte-Carlo Scheme for Semilinear PDEs and BSDEs with Large Scale Parallelization on GPUs 2023

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