Optimal investment and consumption under logarithmic utility and uncertainty model

TL;DR

This paper investigates a robust utility maximization problem with logarithmic utility in incomplete markets, using quadratic BSDEs to characterize optimal solutions under stochastic constraints.

Contribution

It introduces a novel approach to solve robust utility maximization with non-convex constraints via quadratic BSDEs.

Findings

Optimal solutions characterized by quadratic BSDEs.

Applicable to incomplete markets with stochastic constraints.

Provides a framework for robust utility maximization under uncertainty.

Abstract

We study a robust utility maximization problem in the case of an incomplete market and logarithmic utility with general stochastic constraints, not necessarily convex. Our problem is equivalent to maximizing of nonlinear expected logarithmic utility. We characterize the optimal solution using quadratic BSDE.