The adapted solution and comparison theorem for backward stochastic differential equations with Poisson jumps and applications

Juliang Yin, Xuerong Mao, NSF of Guangdong Province (Funder)

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)
183 Downloads (Pure)


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 languageEnglish
Pages (from-to)345-358
Number of pages13
JournalJournal of Mathematical Analysis and Applications
Issue number2
Publication statusPublished - 15 Oct 2008


  • backward stochastic differential equations
  • poisson point process
  • comparison theorem
  • Feynman–Kac formula
  • viscosity solution
  • PDIEs

Cite this