Numeraire-invariant quadratic hedging and mean–variance portfolio allocation

Aleš Černý, Christoph Czichowsky and Jan Kallsen

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

Abstract: The paper investigates quadratic hedging in a general 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 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.

Keywords: mean–variance portfolio selection; quadratic hedging; numeraire change; oblique projection; opportunity-neutral measure; mean–variance hedging (search for similar items in EconPapers)
JEL-codes: C61 G11 G12 (search for similar items in EconPapers)
Pages: 35 pages
Date: 2021
New Economics Papers: this item is included in nep-ore and nep-rmg
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Downloads: (external link)
http://eprints.lse.ac.uk/112612/ Open access 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 (2023)
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Persistent link: https://EconPapers.repec.org/RePEc:ehl:lserod:112612

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