The Two Quantifications of Financial Theory: A Toy Model

38 Pages Posted: 8 Aug 2022 Last revised: 20 Feb 2024

See all articles by Christian Pierre Walter

Christian Pierre Walter

Ecole des Hautes Etudes en Sciences Sociales (EHESS); Institut d'éthique appliquée (IDEA); Université Paris 1 Panthéon-Sorbonne

Date Written: August 2, 2022


I present without mathematical complexity a toy model of the Efficient Market Hypothesis (EMH) that illuminates the correspondences between the multiple representations of EMH with a focus on the two main mathematical frameworks of EMH : the mean-variance universe of Markowitz (1952) under the "real world" probability P and the martingale pricing universe of Harrison and Kreps (1979) and Harrison and Pliska (1981) under the "risk-neutral" probability Q. These two mathematical frameworks have been characterised in Chiapello and Walter (2016) as two quantification conventions. My toy model expands and elaborates on the previous article by adding to it a simplified integrated approach to these two conventions, and linking them to general equilibrium theory. One epistemic gain of the toy model is that it easily captures one of the most difficult conceptual aspects of the EMH, saying the uniqueness of the risk-neutral probability Q in a complete arbitrage-free market.

Keywords: Efficient Market Hypothesis, Toy model, Financial theory, Risk neutral pricing, Fair value

Suggested Citation

Walter, Christian Pierre, The Two Quantifications of Financial Theory: A Toy Model (August 2, 2022). Available at SSRN:

Christian Pierre Walter (Contact Author)

Ecole des Hautes Etudes en Sciences Sociales (EHESS) ( email )

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Paris, 75006

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Institut d'éthique appliquée (IDEA) ( email )

2214 Pavillon J-A. DeSeve
Quebec, Quebec G1K 7P4

Université Paris 1 Panthéon-Sorbonne ( email )

Centre de philosophie contemporaine de la Sorbonne
5, Place du Panthéon
Paris, Ile-de-France 75005

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