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 andthe 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.
Original language | English |
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Pages (from-to) | 345-358 |
Number of pages | 13 |
Journal | Journal of Mathematical Analysis and Applications |
Volume | 346 |
Issue number | 2 |
DOIs | |
Publication status | Published - 15 Oct 2008 |
Keywords
- backward stochastic differential equations
- poisson point process
- comparison theorem
- Feynman–Kac formula
- viscosity solution
- PDIEs