CIRJE-F-1047 "Anticipated Backward SDEs with Jumps and Quadratic-Exponential Growth Drivers"
Author Name

Fujii, Masaaki and Akihiko Takahashi

Date May 2017
Full Paper PDF file 
Remarks Revised in May 2017, March 2018 and July 2018; forthcoming in Stochastics and Dynamics

In this paper, we study a class of Anticipated Backward Stochastic Differential Equations (ABSDE) with jumps. The solution of the ABSDE is a triple (Y,Z, ψ) where Y is a semimartingale, and (Z, ψ) are the diffusion and jump coefficients. We allow the driver of the ABSDE to have linear growth on the uniform norm of Y ’s future paths, as well as quadratic and exponential growth on the spot values of (Z, ψ), respectively. The existence of the unique solution is proved for Markovian and non-Markovian settings with different structural assumptions on the driver. In the former case, some regularities on (Z, ψ) with respect to the forward process are also obtained.