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Donsker-Type Theorem for BSDEs

Philippe Briand · Bernard Delyon · Jean Mémin

108 citations0/0 files storedElectronic Communications in Probability

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Stochastic processes and financial applications Stochastic processes and statistical mechanics Fuzzy Systems and Optimization

Abstract

This paper is devoted to the proof of Donsker's theorem for backward stochastic differential equations (BSDEs for short). The main objective is to give a simple method to discretize in time a BSDE. Our approach is based upon the notion of ``convergence of filtrations'' and covers the case of a $(y,z)$-dependent generator.

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References

1990Adapted solution of a backward stochastic differential equation 1997Backward Stochastic Differential Equations in Finance 2005Backward stochastic differential equations and quasilinear parabolic partial differential equations 1994Solving forward-backward stochastic differential equations explicitly — a four step scheme 2007Forward-Backward Stochastic Differential Equations and their Applications 1991Probabilistic interpretation for systems of quasilinear parabolic partial differential equations 1996Numerical methods for forward-backward stochastic differential equations 1997Non-linear pricing theory and backward stochastic differential equations

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2012Least-Squares Monte Carlo for Backward SDEs 2015A Fourier Cosine Method for an Efficient Computation of Solutions to BSDEs 2008On Numerical Approximations of Forward-Backward Stochastic Differential Equations 2014Simulation of BSDEs by Wiener chaos expansion 2002On the robustness of backward stochastic differential equations

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