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Journal ArticleDOI

The Efficiency Analysis of Choices Involving Risk

01 Jul 1969-The Review of Economic Studies (Oxford University Press)-Vol. 36, Iss: 3, pp 335-346
TL;DR: In this paper, an analysis of the first step of the decision-making process of an individual decision maker among alternative risky ventures is presented, in terms of a single dimension such as money, both for the utility functions and for the probability distributions.
Abstract: Publisher Summary The choice of an individual decision maker among alternative risky ventures may be regarded as a two-step procedure. The decision maker chooses an efficient set among all available portfolios, independently of his tastes or preferences. Then, the decision maker applies individual preferences to this set to choose the desired portfolio. The subject of this chapter is the analysis of the first step. It deals with optimal selection rules that minimize the efficient set by discarding any portfolio that is inefficient in the sense that it is inferior to a member of the efficient set, from point of view of each and every individual, when all individuals' utility functions are assumed to be of a given general class of admissible functions. The analysis presented in the chapter is carried out in terms of a single dimension such as money, both for the utility functions and for the probability distributions. However, the results may easily be extended, with minor changes in the theorems and the proofs, to the multivariate case. The chapter explains a necessary and sufficient condition for efficiency, when no further restrictions are imposed on the utility functions. It presents proofs of the optimal efficiency criterion in the presence of general risk aversion, that is, for concave utility functions.
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

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, the first-, second-and third-order stochastic dominance rules are discussed with an emphasis on the development in the area since the 1980s, focusing on the early 1970s.
Abstract: While Stochastic Dominance has been employed in various forms as early as 1932, it has only been since 1969-1970 that the notion has been developed and extensively employed in the area of economics, finance, agriculture, statistics, marketing and operations research. In this survey, the first-, second-and third-order stochastic dominance rules are discussed with an emphasis on the development in the area since the 1980s.

879 citations

Journal ArticleDOI
Vijay S. Bawa1
TL;DR: In this article, the Third Order Stochastic Dominance (TSD) rule is shown to be the optimal rule when comparing uncertain prospects with equal means, and in the general case of unequal means, no known selection rule uses both necessary and sufficient conditions for dominance.

831 citations

Journal ArticleDOI
TL;DR: In this article, the stochastic specification of input-output response is examined and several postulates are set forth which seem reasonable on the basis of a priori theorizing and observed behavior.

711 citations

References
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Journal ArticleDOI
TL;DR: In this paper, the authors present a body of positive microeconomic theory dealing with conditions of risk, which can be used to predict the behavior of capital marcets under certain conditions.
Abstract: One of the problems which has plagued thouse attempting to predict the behavior of capital marcets is the absence of a body of positive of microeconomic theory dealing with conditions of risk/ Althuogh many usefull insights can be obtaine from the traditional model of investment under conditions of certainty, the pervasive influense of risk in finansial transactions has forced those working in this area to adobt models of price behavior which are little more than assertions. A typical classroom explanation of the determinationof capital asset prices, for example, usually begins with a carefull and relatively rigorous description of the process through which individuals preferences and phisical relationship to determine an equilibrium pure interest rate. This is generally followed by the assertion that somehow a market risk-premium is also determined, with the prices of asset adjusting accordingly to account for differences of their risk.

17,922 citations

Journal ArticleDOI
TL;DR: In this paper, the authors suggest that an important class of reactions of individuals to risk can be rationalized by a rather simple extension of orthodox utility analysis, i.e., individuals frequently must, or can, choose among alternatives that differ, among other things, in the degree of risk to which the individual will be subject.
Abstract: T vHE purpose of this paper is to suggest that an important class of reactions of individuals to risk can be rationalized by a rather simple extension of orthodox utility analysis. Individuals frequently must, or can, choose among alternatives that differ, among other things, in the degree of risk to which the individual will be subject. The clearest examples are provided by insurance and gambling. An individual who buys fire insurance on a house he owns is accepting the certain loss of a small sum (the insurance premium) in preference to the combination of a small chance of a much larger loss (the value of the house) and a large chance of no loss. That is, he is choosing certainty in preference to uncertainty. An individual who buys a lottery ticket is subjecting himself to a large chance of losing a small amount (the price of the lottery ticket) plus a small chance of winning a large amount (a prize) in preference to avoiding both risks. He is choosing uncertainty in preference to certainty.

2,865 citations

Journal ArticleDOI
TL;DR: In this article, the existence of probability distributions with given marginals is studied under typically weaker assumptions, than those which are required by the use of Theorem 1, and necessary and sufficient conditions for a sequence of probability measures to be the sequence of distributions of a martingale, an upper semi-martingale or of partial sums of independent random variables.
Abstract: First an integral representation of a continuous linear functional dominated by a support function in integral form is given (Theorem 1). From this the theorem of Blackwell-Stein-Sherman-Cartier [2], [20], [4], is deduced as well as a result on capacities alternating of order 2 in the sense of Choquet [5], which includes Satz 4.3 of [23] and a result of Kellerer [10], [12], under somewhat stronger assumptions. Next (Theorem 7), the existence of probability distributions with given marginals is studied under typically weaker assumptions, than those which are required by the use of Theorem 1. As applications we derive necessary and sufficient conditions for a sequence of probability measures to be the sequence of distributions of a martingale (Theorem 8), an upper semi-martingale (Theorem 9) or of partial sums of independent random variables (Theorem 10). Moreover an alternative definition of Levy-Prokhorov's distance between probability measures in a complete separable metric space is obtained (corollary of Theorem 11). Section 6 can be read independently of the former sections.

1,191 citations