Constrained portfolio-consumption strategies with uncertain parameters and borrowing costs

TL;DR

This paper investigates optimal portfolio and consumption strategies under model uncertainty, constraints, and differing borrowing and lending rates, providing explicit solutions and analyzing their properties over time.

Contribution

It introduces explicit solutions for robust utility maximization with constraints, accounting for uncertain market parameters and asymmetric borrowing costs.

Findings

Uncertain market parameters significantly affect optimal strategies.

Constraints influence the time evolution of strategies.

Borrowing costs impact the optimal portfolio and consumption choices.

Abstract

This paper studies the properties of the optimal portfolio-consumption strategies in a {finite horizon} robust utility maximization framework with different borrowing and lending rates. In particular, we allow for constraints on both investment and consumption strategies, and model uncertainty on both drift and volatility. With the help of explicit solutions, we quantify the impacts of uncertain market parameters, portfolio-consumption constraints and borrowing costs on the optimal strategies and their time monotone properties.