Yin, J. and Mao, X. and , NSF of Guangdong Province (Funder) (2008) *The adapted solution and comparison theorem for backward stochastic differential equations with Poisson jumps and applications.* Journal of Mathematical Analysis and Applications, 346 (2). pp. 345-358. ISSN 0022-247X

## Abstract

This paper deals with a class of backward stochastic differential equations with Poisson jumps and with random terminal times. We prove the existence and uniqueness result of adapted solution for such a BSDE under the assumption of non-Lipschitzian coefficient. We also derive two comparison theorems by applying a general Girsanov theorem and the linearized technique on the coefficient. By these we first show the existence and uniqueness of minimal solution for one-dimensional BSDE with jumps when its coefficient is continuous and has a linear growth. Then we give a general Feynman-Kac formula for a class of parabolic types of second-order partial differential and integral equations (PDIEs) by using the solution of corresponding BSDE with jumps. Finally, we exploit above Feynman-Kac formula and related comparison theorem to provide a probabilistic formula for the viscosity solution of a quasi-linear PDIE of parabolic type.

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