Scalarized Utility-Based Multi-Asset Risk Measures
29 Pages Posted: 20 Sep 2021 Last revised: 13 Sep 2023
Date Written: September 15, 2021
We present a dual representation for a map that generalizes classical risk measures and has not been analysed so far. It unifies dual representations for well-known risk measures. As a special case, we introduce a risk measure that simultaneously allows to minimise hedging costs and maximize expected utility in the presence of a risk constraint. We call it the scalarized utility-based multi-asset (SUBMA) risk measure. For the SUBMA risk measure we state the following results: If the utility function has constant relative risk aversion and the risk constraint is coherent, then the SUBMA risk measure is coherent. In a one-period financial market setup, we present a sufficient condition for the SUBMA risk measure to be finite-valued. Finally, we derive results about the existence of optimal payoffs.
Keywords: Multi-asset risk measure, portfolio optimization, utility maximization, certainty equivalent, capital adequacy test
JEL Classification: C65, G11, G32
Suggested Citation: Suggested Citation