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Rules for Ordering Uncertain Prospects

01 Jan 1969-The American Economic Review (American Economic Association)-Vol. 59, Iss: 1, pp 25-34
About: This article is published in The American Economic Review.The article was published on 1969-01-01 and is currently open access. It has received 1748 citations till now.
Citations
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Journal ArticleDOI
TL;DR: In this paper, the problem of comparing two frequency distributions f(u) of an attribute y which for convenience I shall refer to as income is defined as a risk in the theory of decision-making under uncertainty.

5,002 citations


Cites background from "Rules for Ordering Uncertain Prospe..."

  • ...3 See Rothschild and Stiglitz [13], Hadar and Russell [ 5 ], and Hanoch and Levy [6]....

    [...]

Journal ArticleDOI
TL;DR: The authors tried to answer the question: When is a random variable Y "more variable" than another random variable X "less variable" by asking when a variable X is more variable than another variable Y.

3,655 citations

Journal ArticleDOI
TL;DR: In this paper, a cardinal utility theory with an associated set of axioms is presented, which is a generalization of the von Neumann-Morgenstern expected utility theory, which permits the analysis of phenomena associated with the distortion of subjective probability.
Abstract: A new theory of cardinal utility, with an associated set of axioms, is presented. It is a generalization of the von Neumann-Morgenstern expected utility theory, which permits the analysis of phenomena associated with the distortion of subjective probability.

2,962 citations

Book
24 Sep 2009
TL;DR: The authors dedicate this book to Julia, Benjamin, Daniel, Natan and Yael; to Tsonka, Konstatin and Marek; and to the Memory of Feliks, Maria, and Dentcho.
Abstract: List of notations Preface to the second edition Preface to the first edition 1. Stochastic programming models 2. Two-stage problems 3. Multistage problems 4. Optimization models with probabilistic constraints 5. Statistical inference 6. Risk averse optimization 7. Background material 8. Bibliographical remarks Bibliography Index.

2,443 citations


Cites methods from "Rules for Ordering Uncertain Prospe..."

  • ...The notion of stochastic ordering or stochastic dominance of first order has been introduced in statistics in Mann and Whitney [150], and Lehmann [142], and further applied and developed in economics (see Quirk and Saposnik [199], Fishburn [77] and Hadar and Russell [94]....

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Book
28 Jun 1987
TL;DR: In this article, the authors provide access to a broad area of research that is not available in separate articles or books of readings, such as the meaning and measurement of risk, general single-period portfolio problems, mean-variance analysis and the Capital Asset Pricing Model, the Arbitrage Pricing Theory, complete markets, multi period portfolio problems and the Intertemporal Capital Asset pricing model, the Black-Scholes option pricing model and contingent claims analysis, 'risk-neutral' pricing with Martingales, Modigliani-Miller and the capital structure of the firm, interest
Abstract: Based on courses developed by the author over several years, this book provides access to a broad area of research that is not available in separate articles or books of readings. Topics covered include the meaning and measurement of risk, general single-period portfolio problems, mean-variance analysis and the Capital Asset Pricing Model, the Arbitrage Pricing Theory, complete markets, multiperiod portfolio problems and the Intertemporal Capital Asset Pricing Model, the Black-Scholes option pricing model and contingent claims analysis, 'risk-neutral' pricing with Martingales, Modigliani-Miller and the capital structure of the firm, interest rates and the term structure, and others.

1,803 citations

References
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Book
01 Jan 1944
TL;DR: Theory of games and economic behavior as mentioned in this paper is the classic work upon which modern-day game theory is based, and it has been widely used to analyze a host of real-world phenomena from arms races to optimal policy choices of presidential candidates, from vaccination policy to major league baseball salary negotiations.
Abstract: This is the classic work upon which modern-day game theory is based. What began more than sixty years ago as a modest proposal that a mathematician and an economist write a short paper together blossomed, in 1944, when Princeton University Press published "Theory of Games and Economic Behavior." In it, John von Neumann and Oskar Morgenstern conceived a groundbreaking mathematical theory of economic and social organization, based on a theory of games of strategy. Not only would this revolutionize economics, but the entirely new field of scientific inquiry it yielded--game theory--has since been widely used to analyze a host of real-world phenomena from arms races to optimal policy choices of presidential candidates, from vaccination policy to major league baseball salary negotiations. And it is today established throughout both the social sciences and a wide range of other sciences.

19,337 citations

Book ChapterDOI
TL;DR: In this article, a comparison is made of several definitions of ordered sets of distributions, some of which were introduced earlier by the author [7], [8] and by Rubin [10], and the results are applied to obtaining tests that give a certain guaranteed power with a minimum number of observations.
Abstract: A comparison is made of several definitions of ordered sets of distributions, some of which were introduced earlier by the author [7], [8] and by Rubin [10]. These definitions attempt to make precise the intuitive notion that large values of the parameter which labels the distributions go together with large values of the random variables themselves. Of the various definitions discussed the combination of two, (B) and (C) of Section 2, appears to be statistically most meaningful. In Section 3 it is shown that this ordering implies monotonicity for the power function of sequential probability ratio tests. In Section 4 the results are applied to obtaining tests that give a certain guaranteed power with a minimum number of observations. Finally, in Section 5, certain consequences are derived regarding the comparability of experiments in the sense of Blackwell [1].

397 citations

Journal ArticleDOI
TL;DR: In this article, a dynamic inventory model is formulated in which the demand distributions may change from period to period, and the optimal policy at each stage is characterized by a single critical number which also could vary in successive periods.
Abstract: A dynamic inventory model is formulated in which the demand distributions may change from period to period. The optimal policy at each stage is characterized by a single critical number which also could vary in successive periods. The dependence of the critical numbers as a function of stochastic ordering amongst distributions is developed under various conditions. Most of the studies are conducted under the assumption of linear purchasing cost. In §3 the possibility of convex purchasing cost is allowed.

303 citations