Nonlinear Feynman-Kac formula and discrete-functional-type BSDEs with continuous coefficients

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:112

Article

Hu, Y ; Ma, J

关键词: backward SDEs with continuous coefficients;    discrete-functionals;    nonlinear Feynman-Kac formulae;    measurable selections;   

DOI  :  10.1016/j.spa.2004.02.002

来源: Elsevier

【 摘 要 】

In this paper, we study a class of multi-dimensional backward stochastic differential equations (BSDEs, for short) in which the terminal values and the generators are allowed to be discrete-functionals of a forward diffusion. We first establish some new types of Feynman-Kac formulas related to such BSDEs under various regularity conditions, and then we prove that under only bounded continuous assumptions on the generators, the adapted solution to such BSDEs does exist. Our result on the existence of the solutions to higher-dimensional BSDEs is new, and our representation theorem is the first step towards the long-standing functional-type Feynman-Kac formula. (C) 2004 Elsevier B.V. All rights reserved.

【 授权许可】

Free