Articlehybrid2002

BSDE associated with Lévy processes and application to PDIE

Khaled Bahlali · Mhamed Eddahbi · El Hassan Essaky

59 citations0/0 files storedInternational Journal of Stochastic Analysis

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

Abstract

We deal with backward stochastic differential equations (BSDE for short) driven by Teugel's martingales and an independent Brownian motion. We study the existence, uniqueness and comparison of solutions for these equations under a Lipschitz as well as a locally Lipschitz conditions on the coefficient. In the locally Lipschitz case, we prove that if the Lipschitz constant LN behaves as log(N) in the ball B(0,N), then the corresponding BSDE has a unique solution which depends continuously on the on the coefficient and the terminal data. This is done with an unbounded terminal data. As application, we give a probabilistic interpretation for a large class of partial differential integral equations (PDIE for short).

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References

2005Stochastic Integration and Differential Equations 1990Adapted solution of a backward stochastic differential equation 1997Backward Stochastic Differential Equations in Finance 1990Stochastic Integration and Differential Equations 1991Probabilistic interpretation for systems of quasilinear parabolic partial differential equations 2000Chaotic and predictable representations for Lévy processes 1997On solutions of backward stochastic differential equations with jumps and applications 2001Backward Stochastic Differential Equations and Feynman-Kac Formula for Levy Processes, with Applications in Finance

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