Parametric multi‐attribute utility functions for optimal profit under risk constraints

Parametric multi‐attribute utility functions for optimal profit under risk constraints

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Article ID: iaor2012292
Volume: 72
Issue: 2
Start Page Number: 257
End Page Number: 271
Publication Date: Feb 2012
Journal: Theory and Decision
Authors: , ,
Keywords: risk, optimization, decision theory
Abstract:

We provide an economic interpretation of the practice consisting in incorporating risk measures as constraints in an expected prospect maximization problem. For what we call the infimum of expectations class of risk measures, we show that if the decision maker (DM) maximizes the expectation of a random prospect under constraint that the risk measure is bounded above, he then behaves as a ‘generalized expected utility maximizer’ in the following sense. The DM exhibits ambiguity with respect to a family of utility functions defined on a larger set of decisions than the original one; he adopts pessimism and performs first a minimization of expected utility over this family, then performs a maximization over a new decisions set. This economic behaviour is called ‘maxmin under risk’ and studied by Maccheroni (2002). As an application, we make the link between an expected prospect maximization problem, subject to conditional value‐at‐risk being less than a threshold value, and a non‐expected utility economic formulation involving ‘loss aversion’‐type utility functions.

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