Numeraire-invariant quadratic hedging and mean–variance portfolio allocation

Černý, Aleš, Czichowsky, Christoph and Kallsen, Jan (2021) Numeraire-invariant quadratic hedging and mean–variance portfolio allocation. .

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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.

Item Type:	Monograph (Working Paper)
Additional Information:	© 2021 The Authors
Divisions:	Mathematics
Subjects:	H Social Sciences > HG Finance
JEL classification:	G - Financial Economics > G1 - General Financial Markets > G11 - Portfolio Choice; Investment Decisions G - Financial Economics > G1 - General Financial Markets > G12 - Asset Pricing; Trading volume; Bond Interest Rates C - Mathematical and Quantitative Methods > C6 - Mathematical Methods and Programming > C61 - Optimization Techniques; Programming Models; Dynamic Analysis
Date Deposited:	15 Nov 2021 16:57
Last Modified:	09 Nov 2023 11:27
URI:	http://eprints.lse.ac.uk/id/eprint/112612

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