Optimal investment and consumption under $g$- expected utility and general constraints in incomplete market

TL;DR

This paper addresses utility maximization in incomplete markets with nonlinear expectations and constraints, providing explicit solutions via $g$-martingales and quadratic BSDEs for various utility functions.

Contribution

It introduces a $g$-martingale approach to solve the utility maximization problem under general constraints in incomplete markets, extending existing methods.

Findings

Explicit solutions for utility maximization under nonlinear expectations.

Characterization of optimal strategies via quadratic BSDEs.

Applicability to various utility functions.

Abstract

This article studies the problem of utility maximization in an incomplete market under a class of nonlinear expectations and general constraints on trading strategies. Using a $g$-martingale method, we provide an explicit solution to our optimization problem for different utility functions and characterize an optimal investment-consumption strategy through the solutions to quadratic BSDEs.