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Uncertainty, Expectations, and Financial InstabilityReviving Allais's Lost Theory of Psychological Time$
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Eric Barthalon

Print publication date: 2014

Print ISBN-13: 9780231166287

Published to Columbia Scholarship Online: November 2015

DOI: 10.7312/columbia/9780231166287.001.0001

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Downside Potential Under Risk

Downside Potential Under Risk

The Allais Paradox and Its Conflicting Interpretations

(p.201) Chapter Ten Downside Potential Under Risk
Uncertainty, Expectations, and Financial Instability

Eric Barthalon

Columbia University Press

This chapter focuses on the psychological importance of downside risk by presenting Maurice Allais's paradox and by contrasting how Allais and prospect theory have interpreted this paradox. It also considers whether the HRL formulation can be used to model how financial market participants form “expectations” of the dispersion of returns under uncertainty. The chapter begins with a brief overview of expected utility theory, with particular emphasis on the Saint Petersburg paradox and how it was resolved by Daniel Bernoulli in 1738. It then considers the Allais paradox and its conflicting interpretations, including prospect theory. It also offers a critique of prospect theory and goes on to discuss Allais's interpretation of his paradox, paying special attention to his invariant cardinal utility function. The chapter concludes with an assessment of the utility of a risky prospect.

Keywords:   downside risk, Maurice Allais, prospect theory, HRL formulation, expectations, expected utility theory, Saint Petersburg paradox, Daniel Bernoulli, Allais paradox, cardinal utility function

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