|CIRJE-F-1047||"Anticipated Backward SDEs with Jumps and Quadratic-Exponential Growth Drivers"|
Fujii, Masaaki and Akihiko Takahashi
|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.