Numeraire-Invariant Quadratic Hedging and Mean–Variance Portfolio Allocation

Aleš Černý, Christoph Czichowsky () and Jan Kallsen ()
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Christoph Czichowsky: London School of Economics and Political Science, London WC2A 2AE, United Kingdom
Jan Kallsen: Christian-Albrechts-Universität zu Kiel, 24118 Kiel, Germany

Mathematics of Operations Research, 2024, vol. 49, issue 2, 752-781

Abstract: The paper investigates quadratic hedging in a semimartingale market that does not necessarily contain a risk-free asset. An equivalence result for hedging with and without numeraire change is established. This permits direct computation of the optimal strategy without choosing a reference asset and/or performing a numeraire change. New explicit expressions for optimal strategies are obtained, featuring the use of oblique projections that provide unified treatment of the case with and without a risk-free asset. The analysis yields a streamlined computation of the efficient frontier for the pure investment problem in terms of three easily interpreted processes. The main result advances our understanding of the efficient frontier formation in the most general case in which a risk-free asset may not be present. Several illustrations of the numeraire-invariant approach are given.

Keywords: Primary: 91G10; 93E20; secondary 15A10; quadratic hedging; numeraire change; oblique projection; mean–variance portfolio selection; no risk-free asset (search for similar items in EconPapers)
Date: 2024
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http://dx.doi.org/10.1287/moor.2023.1374 (application/pdf)

Related works:
Working Paper: Numeraire-invariant quadratic hedging and mean--variance portfolio allocation (2023)
Working Paper: Numeraire-invariant quadratic hedging and mean–variance portfolio allocation (2021)
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:49:y:2024:i:2:p:752-781

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