Composing Tradeoff Studies under Uncertainty based on Parameterized Efficient Sets and Stochastic Dominance Principles

2012 ◽  
Vol 5 (2) ◽  
pp. 418-429 ◽  
Author(s):  
Christopher Bily ◽  
Richard Malak
Keyword(s):  
Stochastic Dominance ◽  
Efficient Sets

scholarly journals Stochastic dominance theory for location-scale family

2006 ◽  
Vol 2006 ◽  
pp. 1-10 ◽  
Author(s):  
Wing-Keung Wong
Keyword(s):  
Stochastic Dominance ◽  
Indifference Curve ◽  
Efficient Set ◽  
Alternative Proof ◽  
Efficient Sets ◽  
Scale Parameters ◽  
General Utility ◽  
The Mean ◽  
Mean Variance ◽  
Variance Criterion

Meyer (1987) extended the theory of mean-variance criterion to include the comparison among distributions that differ only by location and scale parameters and to include general utility functions with only convexity or concavity restrictions. In this paper, we make some comments on Meyer's paper and extend the results from Tobin (1958) that the indifference curve is convex upwards for risk averters, concave downwards for risk lovers, and horizontal for risk neutral investors to include the general conditions stated by Meyer (1987). We also provide an alternative proof for the theorem. Levy (1989) extended Meyer's results by introducing some inequality relationships between the stochastic-dominance and the mean-variance efficient sets. In this paper, we comment on Levy's findings and show that these relationships do not hold in certain situations. We further develop some properties among the first- and second-degree stochastic dominance efficient sets and the mean-variance efficient set.

scholarly journals STOCHASTIC DOMINANCE: CONVEXITY AND SOME EFFICIENCY TESTS

2012 ◽  
Vol 15 (05) ◽  
pp. 1250036 ◽  
Author(s):  
ANDREY LIZYAYEV
Keyword(s):  
Linear Programming ◽  
Relative Risk ◽  
Risk Aversion ◽  
Stochastic Dominance ◽  
Convex Sets ◽  
Relative Risk Aversion ◽  
Third Order ◽  
Efficient Sets ◽  
The Third ◽  
Order Stochastic Dominance

This paper points out the importance of Stochastic Dominance (SD) efficient sets being convex. We review classic convexity and efficient set characterization results on SD efficiency of a given portfolio relative to a diversified set of assets and generalize them in the following aspects. First, we propose a linear programming SSD test that is more efficient than that of Post (2003). Secondly, we expand the SSD efficiency criteria developed by Dybvig and Ross (1982) onto the Third Order Stochastic Dominance and further to Decreasing Absolute and Increasing Relative Risk Aversion Stochastic Dominance. The efficient sets for those are finite unions of convex sets.

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