The Stability of the Constrained Utility Maximization Problem - A BSDE Approach

TL;DR

This paper investigates the stability of a constrained utility maximization problem in financial markets by linking it to backward stochastic differential equations, analyzing how various parameters affect optimal investment strategies.

Contribution

It introduces a novel approach connecting utility maximization with quadratic BSDEs to study sensitivity and convergence of solutions under constraints.

Findings

Proves convergence of primal and dual optimizers in the semimartingale topology.

Extends dual domain descriptions for utility maximization.

Establishes stability results for constrained optimization problems.

Abstract

This article studies the sensitivity of the power utility maximization problem with respect to the investor's relative risk aversion, the statistical probability measure, the investment constraints and the market price of risk. We extend previous descriptions of the dual domain then exploit the link between the constrained utility maximization problem and continuous semimartingale quadratic BSDEs to reduce questions on sensitivity to results on stability for such equations. This then allows us to prove appropriate convergence of the primal and dual optimizers in the semimartingale topology.