City Research Online

Abstract

The law of one price (LOP) broadly asserts that identical financial flows should command the same price. We show that, when properly formulated, 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 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 to give a version of the “Fundamental Theorem of Asset Pricing” appropriate in the quadratic context, establishing the equivalence of the economic concept of 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.

Publication Type:	Article
Additional Information:	This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://link.springer.com/journal/780
Publisher Keywords:	Law of one price, E -density, efficient frontier, mean–variance portfolio selection, quadratic hedging
Subjects:	H Social Sciences > HG Finance
Departments:	Bayes Business School Bayes Business School > Finance
SWORD Depositor:	Symplectic Administrator

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