Stability of exponential utility maximization with respect to market perturbations

TL;DR

This paper studies how small changes in market parameters affect the stability of exponential utility maximization, introducing weaker regularity conditions than previous research to ensure continuity.

Contribution

It establishes continuity of utility maximization under weaker conditions, including a local bmo hypothesis, broadening the applicability of stability results.

Findings

Continuity holds under weaker regularity assumptions.

Weaker conditions include a local bmo hypothesis.

Results apply to markets with bounded bmo norms.

Abstract

We investigate the continuity of expected exponential utility maximization with respect to perturbation of the Sharpe ratio of markets. By focusing only on continuity, we impose weaker regularity conditions than those found in the literature. Specifically, we require, in addition to the $V$-compactness hypothesis of Larsen and \v{Z}itkovi\'c (2007) (ArXiv: 0706.0474), a local $bmo$ hypothesis, a condition which is seen to always be trivially satisfied in the setting of Larsen and \v{Z}itkovi\'c (2007). For markets of the form $S = M + \int \lambda d<M>$, these conditions are simultaneously implied by the existence of a uniform bound on the norm of $\lambda \cdot M$ in a suitable $bmo$ space.