BSDEs driven by infinite dimensional martingales and their applications to stochastic optimal control

摘要

In this paper we consider a backward stochastic differential equation driven by an infinite dimensional martingale. Our aim is to derive the existence and uniqueness of the solution to such an equation. The filtration we consider is an arbitrary right continuous one not necessarily the natural filtration of a Brownian motion, which is furnished usually for the theory of BSDEs. This in particular allows us to study more applications, for example the maximum principle for an optimal control of a stochastic system.