Stochastic dominance with incomplete information on probabilities
To evaluate the expected utility \(Eu(X)=\int u dP\circ X^{-1}\) of a given random prospect X, complete knowledge of the probability P as well as of the decision maker's utility function u is needed. Both are often difficult to assess in practical situations. Under incomplete knowledge, decision between alternative random prospects X and Y may be based on dominance as follows: X is not preferred to Y if \(\int u dP\circ X^{- 1}\leq \int u dP\circ Y^{-1}\) for all u in U and all P in \({\mathcal P}\) where U and \({\mathcal P}\) are sets which are known to contain the ``true'' u and P, respectively. \textit{A. Pearman} and \textit{Z. Kmietowicz} [ibid. 23, 57-63 (1986; Zbl 0581.90041)] have given first results on dominance rules when X and Y are finitely discrete random variables, \({\mathcal P}\) is determined by linear inequalities on probabilities, and U is the set of all increasing or of all increasing and concave functions. The present paper elaborates and clarifies these rules.
scientific article; zbMATH DE number 4172694