PROPOSTA DI UNA FUNZIONE UTILITÀ DIPENDENTE DALL’UTILITÀ ATTESA E DALLA DISPERSIONE DELLE UTILITÀ

Abstract

The author develops the properties and implications of a proposal, con-cerning a summary statistic of the random prospect of utilities. Following a suggestion of Maurice Allais, such a statistic is increasing with expected utility, and decreasing –for most people, who are risk averse – with the mean absolute deviation of utilities; a parameter multiplying this dispersion measure allows for risk averse or risk prone be-haviour, according to its sign, and also for more or less departure from a certain prospect. It is demonstrated that this statistic (a) satisfies the first stochastic dominance,(b) satisfies the independence condition, (c) satisfies the so called “problem of proba-bilistic insurance”, (d) resolves the paradoxes of Allais, Ellsberg and Kahneman-Tver-sky (paradox of the substitution axiom), (e) the mean absolute deviation from the mean cannot be replaced by the standard deviation.