Backward stochastic differential equations and integral-partial differential equations

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

Keywords:

• Backward stochastic differential equations
• jump-diffusion processes
• integral-partial differential operators
• viscosity solutions of systems of partial differential equations

^*The research of this author has been done during a visit at the Université de Provence, and was supported by a grant of the German Deutsche Forschungsgesellschaft

^†Member of the Institut Universitaire de France.13

^*The research of this author has been done during a visit at the Université de Provence, and was supported by a grant of the German Deutsche Forschungsgesellschaft

^†Member of the Institut Universitaire de France.13

Notes

^*The research of this author has been done during a visit at the Université de Provence, and was supported by a grant of the German Deutsche Forschungsgesellschaft

^†Member of the Institut Universitaire de France.13