Expected utility for nonstochastic risk

Ivanenko, Victor and Pasichnichenko, Illia (2016): Expected utility for nonstochastic risk. Forthcoming in: Mathematical Social Sciences

Abstract

Stochastic random phenomena considered in von Neumann – Morgenstern utility theory constitute only a part of all possible random phenomena (Kolmogorov (1986)). We show that any sequence of observed consequences generates a corresponding sequence of frequency distributions, which in general does not have a single limit point but a non-empty closed limit set in the space of finitely additive probabilities. This approach to randomness allows to generalize the expected utility theory in order to cover decision problems under nonstochastic random events. We derive the maxmin expected utility representation for preferences over closed sets of probability measures. The derivation is based on the axiom of preference for stochastic risk, i.e. the decision maker wishes to reduce a set of probability distributions to a single one. This complements Gilboa and Schmeidler’s (1989) consideration of the maxmin expected utility rule with objective treatment of multiple priors.

• Item Type: MPRA Paper
• Language: English
• Keywords: expected utility, risk, mass phenomena, statistical regularity, nonstochastic randomness, multiple prior
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C10 - General; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D81 - Criteria for Decision-Making under Risk and Uncertainty

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