Numeraire-invariant quadratic hedging and mean--variance portfolio allocation

Ale\v{s} \v{C}ern\'y, Christoph Czichowsky and Jan Kallsen
Authors registered in the RePEc Author Service: Aleš Černý

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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 where a risk-free asset may not be present. Several illustrations of the numeraire-invariant approach are given.

Date: 2021-10, Revised 2025-07
New Economics Papers: this item is included in nep-rmg
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Published in Mathematics of Operations Research 49(2), 752-781, 2024

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http://arxiv.org/pdf/2110.09416 Latest version (application/pdf)

Related works:
Journal Article: Numeraire-Invariant Quadratic Hedging and Mean–Variance Portfolio Allocation (2024)
Working Paper: Numeraire-invariant quadratic hedging and mean–variance portfolio allocation (2021)
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2110.09416

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