Constrained NonSmooth Utility Maximization on the Positive Real Line

TL;DR

This paper extends duality theory for utility maximization to incomplete markets with cone constraints and nonsmooth utility functions, proving existence of optimal solutions and simplifying proofs.

Contribution

It introduces a generalized duality framework for constrained, nonsmooth utility maximization, expanding prior theories to more complex market and utility settings.

Findings

Existence of primal and dual optimal solutions established

Duality relationship extended to nonsmooth, constrained utility functions

Simplified proofs for duality in constrained utility maximization

Abstract

We maximize the expected utility of terminal wealth in an incomplete market where there are cone constraints on the investor's portfolio process and the utility function is not assumed to be strictly concave or differentiable. We establish the existence of the optimal solutions to the primal and dual problems and their dual relationship. We simplify the present proofs in this area and extend the existing duality theory to the constrained nonsmooth setting.