Ogryczak, W. & Ruszczynski, A. (1997). From Stochastic Dominance to MeanRisk Models: Semideviations as Risk Measures. IIASA Interim Report. IIASA, Laxenburg, Austria: IR97027

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Abstract
Two methods are frequently used for modeling the choice among uncertain outcomes: stochastic dominance and meanrisk approaches. The former is based on an axiomatic model of riskaverse preferences but does not provide a convenient computational recipe. The latter quantifies the problem in a lucid form of two criteria with possible tradeoff analysis, but cannot model all riskaverse preferences. In particular, if variance is used as a measure of risk, the resulting meanvariance (Markowitz) model is, in general, not consistent with stochastic dominance rules. This paper shows that the standard semideviation (square root of the semivariance) as the risk measure makes the meanrisk model consistent with the second degree stochastic dominance, provided that the tradeoff coefficient is bounded by a certain constant. Similar results are obtained for the absolute semideviation, and for the absolute and standard deviations in the case of symmetric or bounded distributions. In the analysis we use a new tool, the OutcomeRisk diagram, which appears to be particularly useful for comparing uncertain outcomes.
Item Type:  Monograph (IIASA Interim Report) 

Research Programs:  Risk, Modeling, Policy (RMP) 
Depositing User:  IIASA Import 
Date Deposited:  15 Jan 2016 02:09 
Last Modified:  27 Aug 2021 17:16 
URI:  http://pure.iiasa.ac.at/5264 
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