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Numeraire-Invariant Quadratic Hedging and Mean–Variance Portfolio Allocation

Author

Listed:
  • Aleš Černý

    (Bayes Business School, City University of London, London EC1Y 8TZ, United Kingdom)

  • Christoph Czichowsky

    (London School of Economics and Political Science, London WC2A 2AE, United Kingdom)

  • Jan Kallsen

    (Christian-Albrechts-Universität zu Kiel, 24118 Kiel, Germany)

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.

Suggested Citation

  • Aleš Černý & Christoph Czichowsky & Jan Kallsen, 2024. "Numeraire-Invariant Quadratic Hedging and Mean–Variance Portfolio Allocation," Mathematics of Operations Research, INFORMS, vol. 49(2), pages 752-781, May.
    • Handle: RePEc:inm:ormoor:v:49:y:2024:i:2:p:752-781
    DOI: 10.1287/moor.2023.1374
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