Article1997

Backward stochastic differential equations and integral-partial differential equations

Guy Barles A · Rainer Buckdahn · Étienne Pardoux

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Stochastic processes and financial applications Nonlinear Partial Differential Equations Differential Equations and Boundary Problems

Abstract

We consider a backward stochastic differential equation, whose data (the final condition and the coefficient) are given functions of a jump-diffusion process. We prove that under mild conditions the solution of the BSDE provides a viscosity solution of a system of parabolic integral-partial differential equations. Under an additional assumption, that system of equations is proved to have a unique solution, in a given class of continuous functions

Citations in this library

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References

1983Stochastic Differential Equations and Diffusion Processes 1990Adapted solution of a backward stochastic differential equation 2005Backward stochastic differential equations and quasilinear parabolic partial differential equations 1994Necessary Conditions for Optimal Control of Stochastic Systems with Random Jumps

Cited by

2005A Finite Difference Scheme for Option Pricing in Jump Diffusion and Exponential Lévy Models 2009Mean-field backward stochastic differential equations and related partial differential equations 2004Nonlinear Expectations, Nonlinear Evaluations and Risk Measures 2006Backward stochastic differential equations with jumps and related non-linear expectations 2006Second‐order backward stochastic differential equations and fully nonlinear parabolic PDEs 1998Backward Stochastic Differential Equations and Viscosity Solutions of Systems of Semilinear Parabolic and Elliptic PDEs of Second Order 2008Stochastic Differential Games and Viscosity Solutions of Hamilton–Jacobi–Bellman–Isaacs Equations 2006Bounded solutions to backward SDEs with jumps for utility optimization and indifference hedging

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