Numeraire-Invariant Quadratic Hedging and Mean-Variance Portfolio Allocation

arXiv preprint 2110.09416

35 Pages Posted: 19 Oct 2021

See all articles by Aleš Černý

Aleš Černý

Bayes Business School, City, University of London

Christoph Czichowsky

London School of Economics & Political Science (LSE) - Department of Mathematics

Jan Kallsen

CAU Kiel

Date Written: October 18, 2021

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

JEL Classification: G11, G12, C61

Suggested Citation

Černý, Aleš and Czichowsky, Christoph and Kallsen, Jan, Numeraire-Invariant Quadratic Hedging and Mean-Variance Portfolio Allocation (October 18, 2021). arXiv preprint 2110.09416, Available at SSRN: https://ssrn.com/abstract=3944947

Aleš Černý (Contact Author)

Bayes Business School, City, University of London

Northampton Square
London, EC1V 0HB
United Kingdom

Christoph Czichowsky

London School of Economics & Political Science (LSE) - Department of Mathematics ( email )

Houghton Street
GB-London WC2A 2AE
United Kingdom

HOME PAGE: http://https://www.lse.ac.uk/Mathematics/people/Christoph-Czichowsky

Jan Kallsen

CAU Kiel ( email )

Kiel
Germany

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