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Scalarized utility-based multi-asset risk measures

Author

Listed:
  • Sascha Desmettre
  • Christian Laudagé
  • Jörn Sass

Abstract

We introduce a risk measure that simultaneously allows to minimize 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. We derive results about the existence of optimal payoffs. Finally, we present a dual representation for a map that generalizes classical risk measures and has not been analyzed so far. In particular, it gives us the dual representation for the SUBMA risk measure.

Suggested Citation

  • Sascha Desmettre & Christian Laudagé & Jörn Sass, 2025. "Scalarized utility-based multi-asset risk measures," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2025(3), pages 271-299, March.
    • Handle: RePEc:taf:sactxx:v:2025:y:2025:i:3:p:271-299
    DOI: 10.1080/03461238.2024.2410211
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