Further Analysis of the Markowitz Model of Utility with a small degree of probability distortion

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David Peel
David Law


Explanation of the Allais paradox and the preference of many for multiple prize lottery tickets provide a rationale for why a model of agent’s choice under uncertainty should embody the assumption that they distort probabilities. However the degree of probability distortion  required to  explain gambling on long shots in Cumulative Prospect Theory appears problematic since it implies subjective expected rates of return are dramatically higher than objective returns. Here we show that a  Markowitz model of expected utility, supplemented by a small degree of probability distortion, has qualitatively  similar predictions as Cumulative Prospect Theory for numerous experimental outcomes as well as the  indifference curves between expected return and objective probabilities for a given stake gamble. In addition we show how a small degree of probability distortion can lead to a preference  for a multiple prize lottery which has a rather  different prize structure and associated probabilities than the optimally chosen one prize lottery  even though the utility gain is small.

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