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Subjective risk and disappointment

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  • Thierry Chauveau

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

If an investor does care for utilities -and not for monetary outcomes- stochastic dominances should be expressed in terms of utility units ("utils"). If so, any "rational" investor may be characterized by an elementary utility function -called canonical utility function- which is such that the partial weak order induced by stochastic dominance over utils is as "close" to the weak order of preferences as possible. As a consequence, the random utilities of the available prospects do not violate the second-order stochastic dominance property. Substituting utils for monetary units leads to substitute "subjective" risk for "objective" risk à la Rothschild and Stiglitz (1970). A weakened independence axiom may them be set over comparable prospects, i.e. those which exhibit the same canonical expected utility. This leads to a fully choice-based theory of disappointment. The functional is lottery-dependent (Becker and Sarin 1987). When constant marginal utility is assumed, it is but the opposite to a convex measure of risk (Föllmer and Schied 2002). It may be viewed as a theoretical justification for choosing this measure of risk.

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  • Thierry Chauveau, 2012. "Subjective risk and disappointment," Post-Print halshs-00747902, HAL.
    • Handle: RePEc:hal:journl:halshs-00747902
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00747902v3
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    References listed on IDEAS

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    1. Joao L. Becker & Rakesh K. Sarin, 1987. "Lottery Dependent Utility," Management Science, INFORMS, vol. 33(11), pages 1367-1382, November.
    2. Thierry Chauveau & Nicolas Nalpas, 2010. "Disappointment Models: an axiomatic approach," Documents de travail du Centre d'Economie de la Sorbonne 10102, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    3. Graham Loomes & Robert Sugden, 1986. "Disappointment and Dynamic Consistency in Choice under Uncertainty," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(2), pages 271-282.
    4. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
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