Scalarized Utility-Based Multi-Asset Risk Measures

29 Pages Posted: 20 Sep 2021 Last revised: 13 Sep 2023

See all articles by Sascha Desmettre

Sascha Desmettre

Johannes Kepler University Linz

Christian Laudagé

RPTU Kaiserslautern-Landau

Jörn Sass

RPTU Kaiserslautern-Landau

Date Written: September 15, 2021

Abstract

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

Desmettre, Sascha and Laudagé, Christian and Sass, Jörn, Scalarized Utility-Based Multi-Asset Risk Measures (September 15, 2021). Available at SSRN: https://ssrn.com/abstract=3924271 or http://dx.doi.org/10.2139/ssrn.3924271

Sascha Desmettre

Johannes Kepler University Linz ( email )

Altenbergerstr. 69
A-4040 Linz, Upper Austria 4040
Austria

HOME PAGE: http://shorturl.at/dwX47

Christian Laudagé (Contact Author)

RPTU Kaiserslautern-Landau ( email )

Kaiserslautern
Germany

Jörn Sass

RPTU Kaiserslautern-Landau ( email )

Kaiserslautern
Germany

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