Open AccessPROPOSTA DI UNA FUNZIONE UTILITÀ DIPENDENTE DALL’UTILITÀ ATTESA E DALLA DISPERSIONE DELLE UTILITÀ
Author(s) -
Vittorio B. Frosini
Publication year - 2014
Publication title -
rendiconti. classe di lettere e scienze morali e storiche
Language(s) - English
Resource type - Journals
eISSN - 2384-9150
pISSN - 1124-1667
DOI - 10.4081/let.2011.97
Subject(s) - axiom independence , statistic , stochastic dominance , mathematics , mathematical economics , axiom , expected utility hypothesis , prospect theory , absolute deviation , standard deviation , independence (probability theory) , econometrics , statistics , economics , geometry , finance
The author develops the properties and implications of a proposal, concerning 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 behaviour, 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 probabilistic insuranceâ€, (d) resolves the paradoxes of Allais, Ellsberg and Kahneman-Tversky (paradox of the substitution axiom), (e) the mean absolute deviation from the mean cannot be replaced by the standard deviation.