Backward stochastic Volterra integral equations with jumps and some related problems

Abstract

In this paper, we deal with backward stochastic Volterra integral equations with jumps. Firstly, we present the well-posedness of backward stochastic Volterra integral equations with jumps in the sense of adapted M-solution. Secondly, we give some properties of backward stochastic Volterra integral equations with jumps, which contain the duality principle, comparison theorem and the regularity of adapted M-solution. Thirdly, dynamic risk measure by means of backward stochastic Volterra integral equations with jumps is established. Fourthly, a maximum principle of Pontryagin type is obtained for an optimal control problem of stochastic Volterra integral equations with jumps. Finally, we investigate the well-posedness of linear fractional backward stochastic Volterra integral equations.