A SPDE Maximum Principle for Stochastic Differential Games under Partial Information with Application to Optimal Portfolios on Fixed Income Markets

Abstract

In this paper we aim at establishing a necessary and sufficient maximum principle for partial information control of general stochastic games, where the controlled process is given by a stochastic reaction-diffusion equation with jumps. As an application of this result we study a zero-sum stochastic differential game on a fixed income market, that is we solve the problem of finding an optimal strategy for portfolios of constant maturity interest rate derivatives managed by a trader who plays against various "market scenarios". Here we permit the restriction that the trader has limited access to market information.