Optimal investment and consumption under logarithmic utility and uncertainty model

Abstract

We study a robust utility maximization problem in the case of incomplete market and logarithmic utility with general stochastic constraints. Our problem is equivalent to the maximization of nonlinear expected logarithmic utility. We characterize the optimal solution using quadratic backward stochastic differential equations.

Keywords

Backward stochastic differential equations / g-expectation / g-martingale / Logarithmic utility / Robust utility

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