Two recent models of risky decision making developed by Fishburn (Fishbijrn, P. C. 1977. Mean-risk analysis with risk associated with below-target returns. Amer. Econ. Rev. 67 116–126.) and by Kahneman and Tversky (Kahneman, D., A. Tversky. 1979. Prospect theory: an analysis of decisions under risk. Econometrica 47 262–291.) have emphasized the importance of a target return or a reference point in determining preferences and choices among gambles. Target returns and reference points represent variations on the concept of an aspiration level, an old idea in theories of decision making. Additional evidence on the need to incorporate such a concept in the analysis of risky choice behavior is presented in this paper. In three experiments, the relationship of pairs of gambles to an assumed reference point was varied by adding or subtracting a constant amount from all outcomes. The results demonstrate that such translations of outcomes can result in the reversal of choice within pairs of gambles. The effect of such translations on choice depended on whether the size of the translation was sufficient to insure that one gamble in a pair had outcome values either all above or all below the reference point, while the other gamble had outcome values both above and below the reference point. A model of the effects of a reference point on risky choice behavior is presented and the results are also discussed in terms of the Fishburn and Kahneman-Tversky models, as well as other theories of risky decision making.

This paper reports on the risk preferences for below target returns of 224 managers from the U.S. Canada, and Europe. When only non-ruinous losses were involved, 71% of the managers were risk seeking for below target returns. The distribution of risk preferences tended to be stable over a wide range of experimental conditions: diversity of background of the managers, the size of outcomes below target, and the context of the decision process (personal versus managerial). When ruinous losses were introduced for 75 of the managers, 64% switched to risk averse behavior. Empirical findings concerning the relationship between risk preferences for below target returns and several demographic characteristics of managers are also reported.decision making, utility preference, targets

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The purpose of this paper is to present an algorithm for solving the quadratic binary programming problem. Although a problem with this structure may arise in many situations, it is particularly common in capital budgeting when a decision-maker is confronted with a set of investment proposals from which he must select a portfolio. If returns of proposals are intercorrelated random variables and if the decision-maker uses as his criterion for selection the mean μ and variance σ2 of portfolio returns, his decision requires prior identification of the (μ, σ2) efficient set. The algorithm developed to solve the problem and hence necessary to generate the efficient set is based on the concept of implicit enumeration recently introduced by Egon Balas for solution of the binary linear programming problem.

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