The law of one price in quadratic hedging and mean–variance portfolio selection

Černý, Aleš and Czichowsky, Christoph ORCID: 0000-0002-3513-6843 (2025) The law of one price in quadratic hedging and mean–variance portfolio selection. Finance and Stochastics. ISSN 0949-2984

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Abstract

The law of one price (LOP) broadly asserts that identical financial flows should command the same price. We show that when properly formulated, the LOP is the minimal condition for a well-defined mean–variance portfolio allocation framework without degeneracy. Crucially, the paper identifies a new mechanism through which the LOP can fail in a continuous-time L2 -setting without frictions, namely “trading from just before a predictable stopping time”, which surprisingly identifies LOP violations even for continuous price processes. Closing this loophole allows us to give a version of the “fundamental theorem of asset pricing” appropriate in the quadratic context, establishing the equivalence of the economic concept of the LOP with the probabilistic property of the existence of a local ℰ-martingale state price density. The latter provides unique prices for all square-integrable contingent claims in an extended market and subsequently plays an important role in mean–variance portfolio selection and quadratic hedging. Mathematically, we formulate a novel variant of the uniform boundedness principle for conditionally linear functionals on the L0-module of conditionally square-integrable random variables. We then study the representation of time-consistent families of such functionals in terms of stochastic exponentials of a fixed local martingale.

Item Type:	Article
Additional Information:	© 2025 The Author(s)
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics 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:	21 Oct 2024 09:18
Last Modified:	22 Apr 2025 07:54
URI:	http://eprints.lse.ac.uk/id/eprint/125805

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