Risk Apportionment Via Bivariate Stochastic Dominance

Abstract

This paper extends to bivariate utility functions Eeckhoudt, Schlesinger and Tsetlin’s (2009) result for the combination of ‘bad’ and ‘good.’ The decision-maker prefers to get some of the ‘good’ and some of the ‘bad’ to taking a chance on all the ‘good’ or all the ‘bad’ where ‘bad’ is defined via (N,M) - increasing concave order. We generalize the concept of bivariate risk aversion ((N,M)=(1,1)) introduced by Richard (1975) to higher orders. Importantly, in the bivariate framework, preference for lottery [(X N,Y M);(Y N,X M)] to lottery [(X N,X M);(Y N,Y M)] allows us to assert bivariate risk apportionment of order (N,M) and to extend the concept of risk apportionment defined by Eeckhoudt and Schlesinger (2006).