Journal of Applied Mathematics
Volume 2003 (2003), Issue 9, Pages 447-458
doi:10.1155/S1110757X03207075
On the existence of certainty equivalents of various relevant types
1Facultad de Economía y Empresa, Universidad de Salamanca, Salamanca E 37008, Spain
2Dipartimento di Matematica Applicata “Bruno de Finetti,”, Università di Trieste, Piazzale Europa 1, Trieste 34127, Italy
Received 24 July 2002; Revised 5 May 2003
Copyright © 2003 J. C. R. Alcantud and G. Bosi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We tackle the problem of associating certainty equivalents with preferences over stochastic situations, which arises in a number of different fields (e.g., the theory of risk attitudes or the analysis of stochastic cooperative games). We study the possibility of endowing such preferences with certainty equivalence functionals that satisfy relevant requirements (such as positive homogeneity, translation invariance, monotonicity with respect to first-order stochastic dominance, and subadditivity). Uniqueness of the functional is also addressed in fairly general conditions.