Stochastic dominance with incomplete information on probabilities
type: Item
instance of: scholarly article
title: Stochastic dominance with incomplete information on probabilities
zbMATH Open document ID: 0712.90001
DOI: 10.1016/0377-2217(89)90234-8
author: Hans-Jürgen Keppe
author: Martin Weber
published in: European Journal of Operational Research
publication date: 1989-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 91B06
Mathematics Subject Classification ID: 91B16
Mathematics Subject Classification ID: 90B50
zbMATH DE Number: 4172694
zbMATH Keywords: incomplete information
zbMATH Keywords: dominance
reviewed by: Karl Mosler
MaRDI profile type: Publication
full work available at URL: 0377-2217(89)90234-8
OpenAlex ID: W1989283332
cites work: Research Bibliography—Stochastic Dominance: A Research Bibliography
cites work: Characterization of the extreme points of a class of special polyhedra
cites work: Q5528344
cites work: Entscheidungen bei unvollständiger Information
cites work: Stochastic dominance with linear partial information
cites work: Decision making with incomplete information
description: scientific article; zbMATH DE number 4172694