Journal of Applied Mathematics
Volume 2003 (2003), Issue 9, Pages 447-458

On the existence of certainty equivalents of various relevant types

J. C. R. Alcantud1 and G. Bosi2

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.


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.