Ambiguous Risk Measures and Optimal Robust Portfolios

TLDR

The paper addresses robust financial decision‑making under model uncertainty. The study aims to compute worst‑case optimal portfolios that minimize a weighted risk‑mean objective under model ambiguity. Assuming a nominal discrete return distribution and a Kullback–Leibler divergence bound, the authors analyze both variance and absolute deviation risk measures to derive an efficient method for computing worst‑case optimal portfolios.

Abstract

This paper deals with a problem of guaranteed (robust) financial decision-making under model uncertainty. An efficient method is proposed for determining optimal robust portfolios of risky financial instruments in the presence of ambiguity (uncertainty) on the probabilistic model of the returns. Specifically, it is assumed that a nominal discrete return distribution is given, while the true distribution is only known to lie within a distance d from the nominal one, where the distance is measured according to the Kullback–Leibler divergence. The goal in this setting is to compute portfolios that are worst-case optimal in the mean-risk sense, that is, to determine portfolios that minimize the maximum with respect to all the allowable distributions of a weighted risk-mean objective. The analysis in the paper considers both the standard variance measure of risk and the absolute deviation measure.