COMPARING RISKS WITH UNBOUNDED DISTRIBUTIONS

We extend the characterizations of increasing risks developed by Roths child and Stiglitz [Rothschild, M., Stiglitz, J.E., 1970. Increasing r isk, I: A definition, Journal of Economic Theory 2, 225-243.] to the c ase of unbounded probability distributions. It will turn out, that wea k convergence of distributions is insufficient in that case. It has to be replaced by a stronger definition of convergence. We also consider the related notion of increasing risk. about nu introduced by Landsbe rger and Meilijson [Landsberger, M., Meilijson, I., 1990a. A tale of t wo tales: an alternative characterization of comparative risk Journal of Risk and Uncertainty 3, 65-82.; Landsberger, M., I. Meilijson, 1990 b. Lotteries, insurance, and star-shaped utility functions, Journal of Economic Theory 52, 1-17.]. Moreover, for some of the results we give new and more elegant proofs. (C) 1998 Elsevier Science S.A. All right s reserved.