INCOMPLETE INFORMATION WITH RECURSIVE PREFERENCES

Abstract

We consider the case of an agent with recursive preferences (Stochastic Differential Utility or SDU) who cannot observe the random drift of the stock price process. This partial information problem can be transformed into a problem with full information, in which the drift is replaced by its expected value conditional on the information given by the stock price history. We are then in a position to use recent results for maximizing SDUs under full information and their connection to Forward-Backward Stochastic Differential Equations. They enable us to study qualitative differences between the cases with full and partial information. We also analyze some special cases in which we obtain semi-explicit results and compute the SDU numerically.