Scalarized utility-based multi-asset risk measures

39 Pages Posted: 20 Sep 2021

See all articles by Sascha Desmettre

Sascha Desmettre

Johannes Kepler University Linz

Christian Laudagé

Fraunhofer ITWM - Department Financial Mathematics

Jörn Sass

University of Kaiserslautern - Department of Mathematics

Date Written: September 15, 2021

Abstract

Financial institutions have to satisfy capital adequacy tests required, e.g., by the Basel Accords for banks or by Solvency II for insurers. If the financial situation of an institution is tight, then it can happen that no reallocation of the initial endowment would pass the capital adequacy test. The classical portfolio optimization approach breaks down and a capital increase is needed. We introduce the scalarized utility-based multi-asset (SUBMA) risk measure which optimizes the hedging costs and the expected utility of an agent simultaneously subject to the capital adequacy test.
We find that the SUBMA risk measure is coherent if the utility function has constant relative risk aversion and the capital adequacy test leads to a coherent acceptance set. In a one-period financial market model we present a sufficient condition for the SUBMA risk measure to be finite-valued and continuous. Under further assumptions on the utility function we obtain existence and uniqueness results for the optimal hedging strategies. Finally, we calculate the SUBMA risk measure in a continuous-time financial market model for two benchmark capital adequacy tests.

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)

Fraunhofer ITWM - Department Financial Mathematics ( email )

Fraunhofer-Platz 1
Kaiserslautern, 67663
Germany

Jörn Sass

University of Kaiserslautern - Department of Mathematics ( email )

D-67653 Kaiserslautern
Germany

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