Recursive utility maximization under partial information

TL;DR

This paper addresses recursive utility maximization under partial information by transforming it into a full information problem, employing variational formulations, stochastic game theory, and terminal perturbation methods to characterize optimal strategies.

Contribution

It introduces a novel approach to recursive utility maximization under partial information by transforming the problem and applying variational and game-theoretic techniques.

Findings

Explicit saddle points for K-ignorance cases are derived.

A characterization of optimal terminal wealth is provided for smooth generators.

The problem is reformulated under full information, facilitating solution derivation.

Abstract

This paper concerns the recursive utility maximization problem under partial information. We first transform our problem under partial information into the one under full information. When the generator of the recursive utility is concave, we adopt the variational formulation of the recursive utility which leads to a stochastic game problem and a characterization of the saddle point of the game is obtained. Then, we study the K-ignorance case and explicit saddle points of several examples are obtained. At last, when the generator of the recursive utility is smooth, we employ the terminal perturbation method to characterize the optimal terminal wealth.