DYNAMIC UTILITY AND RELATED NONLINEAR SPDES DRIVEN BY LÉVY NOISE

Abstract

In this work, we study a class of consistent dynamic utilities in a incomplete financial market including jumps. First, we show that the dynamic utility is solution of a non-linear second-order stochastic partial integro-differential equation (SPIDE). Second, a complete study of the primal and the dual problems, allows us, firstly, to establish a connection between the utility-SPIDE and two SDEs satisfied by the optimal processes. Based on this connection, stochastic flow technics for SDEs and characteristic method, the SPIDE is completely solved and monotony and concavity properties of the solution are proved.