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.