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

Papers from arXiv.org

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 (Proposition 3.16). This permits direct computation of the optimal strategy without choosing a reference asset and/or performing a numeraire change (Theorem 4.1). 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 (Theorem 4.3). The analysis yields a streamlined computation of the efficient frontier for the pure investment problem in terms of three easily interpreted processes (Equation~1.1). 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 2023-01
New Economics Papers: this item is included in nep-rmg
References: View references in EconPapers View complete reference list from CitEc
Citations:

Published in Mathematics of Operations Research 49(2), 752-781, 2024

Downloads: (external link)
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)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2110.09416

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().