Articlegreen2018

Asymptotic expansion for forward-backward SDEs with jumps

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Stochastic processes and financial applications Nonlinear Differential Equations Analysis Fuzzy Systems and Optimization

Abstract

This work provides a semi-analytic approximation method for decoupled forward-backward SDEs (FBSDEs) with jumps. In particular, we construct an asymptotic expansion method for FBSDEs driven by the random Poisson measures with σ-finite compensators as well as the standard Brownian motions around the small-variance limit of the forward SDE. We provide a semi-analytic solution technique as well as its error estimate for which we only need to solve essentially a system of linear ODEs. In the case of a finite jump measure with a bounded intensity, the method can also handle state-dependent and hence non-Poissonian jumps, which are quite relevant for many practical applications.

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2007Brownian Motion and Stochastic Calculus 2005Stochastic Integration and Differential Equations 1990Adapted solution of a backward stochastic differential equation 1997Backward Stochastic Differential Equations in Finance 2009Lévy Processes and Stochastic Calculus 1972Stochastic Differential Equations 1989Theory of Martingales 2005Backward stochastic differential equations and quasilinear parabolic partial differential equations

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