Comonotonic Book-Making with Nonadditive Probabilities

Abstract

This paper shows how de Finetti's book-making principle, commonly used to justify additive subjective probabilities, can be modified to agree with some nonexpected utility models. More precisely, a new foundation of the rank-dependent models is presented that is based on a comonotonic extension of the book-making principle. The extension excludes book-making only if all gambles considered induce a same rank-ordering of the states of nature through favorableness of their associated outcomes, and allows for nonadditive probabilities. Typical features of rank-dependence, hedging, ambiguity aversion, and pessimism and optimism, can be accommodated.

Keywords: Book-Making, Comonotonic, Choquet expected utility, ambiguity aversion, ordered vector space

JEL Classification: D81, C60