Quadratic-exponential growth backward stochastic Volterra integral equations with jumps and associated dynamic risk measure

Abstract Risk management is one of the fundamental concepts in the mathematical finance. We study quadratic-exponential growth Backward Stochastic Volterra Integral Equations with Jumps (QBSVIEJs, for short). We prove the existence and uniqueness of solutions to QBSVIEJ in two steps. First, we use the fact that a QBSVIEJ with the generator independent of 𝑦 can be represented by a (infinite) family of QBSDEJs to get the first simple well-posedness result. And secondly, we use fixed point argument and induction to deal with the general case. We prove a comparison theorem and, as an application, define a convex dynamic risk measure by means of the QBSVIEJs.