On the Conditional Value-at-Risk probability-dependent utility function

Theory and Decision 68 (1-2):49-68 (2010)

Abstract
The Expected Shortfall or Conditional Value-at-Risk (CVaR) has been playing the role of main risk measure in the recent years and paving the way for an enormous number of applications in risk management due to its very intuitive form and important coherence properties. This work aims to explore this measure as a probability-dependent utility functional, introducing an alternative view point for its Choquet Expected Utility representation. Within this point of view, its main preference properties will be characterized and its utility representation provided through local utilities with an explicit dependence on the assessed revenue’s distribution (quantile) function. Then, an intuitive interpretation for the related probability dependence and the piecewise form of such utility will be introduced on an investment pricing context, in which a CVaR maximizer agent will behave in a relativistic way based on his previous estimates of the probability function. Finally, such functional will be extended to incorporate a larger range of risk-averse attitudes and its main properties and implications will be illustrated through examples, such as the so-called Allais Paradox
Keywords Conditional Value-at-Risk  Probability-dependent utility function  Choquet Expected Utility  Certainty Equivalent  Allais Paradox
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DOI 10.1007/s11238-009-9154-2
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Theory of Games and Economic Behavior.John von Neumann & Oskar Morgenstern - 1945 - Journal of Philosophy 42 (20):550-554.

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