Risk analysis under partial prior information and nonmonotone utility functions

The main objective of the paper is to investigate the risk analysis problems when a precise but unknown probability distribution of states of nature belongs to a set of continuous probability distributions restricted by some known lower and upper distributions and when utility functions are nonmonotone. Methods for choosing optimal distributions among the set of distributions and for computing the expected utilities are proposed. Some special cases of sets of distributions, including possibility distributions, step functions, belief functions are studied under the same conditions. Various numerical examples illustrate the proposed methods.