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Wing-keung Wong - One of the best experts on this subject based on the ideXlab platform.
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farinelli and tibiletti ratio and Stochastic Dominance
Risk Management, 2019Co-Authors: Xu Guo, Cuizhen Niu, Wing-keung WongAbstract:Farinelli and Tibiletti (F–T) ratio, a general risk-reward performance measurement ratio, is popular due to its simplicity and yet generality that both Omega ratio and upside potential ratio are its special cases. The F–T ratios are ratios of average gains to average losses with respect to a target, each raised by a power index, p and q. In this paper, we establish the consistency of F–T ratios with any nonnegative values p and q with respect to first-order Stochastic Dominance. Second-order Stochastic Dominance does not lead to F–T ratios with any nonnegative values p and q, but can lead to F–T Dominance with any $$p<1$$ and $$q\ge 1$$ . Furthermore, higher-order Stochastic Dominance ( $$n\ge 3$$ ) leads to F–T Dominance with any $$p<1$$ and $$q\ge n-1$$ . We also find that when the variables being compared belong to the same location-scale family or the same linear combination of location-scale families, we can get the necessary relationship between the Stochastic Dominance with the F–T ratio after imposing some conditions on the means. There are many advantages of using the F–T ratio over other measures, and academics and practitioners can benefit by using the theory we developed in this paper. For example, the F–T ratio can be used to detect whether there is any arbitrage opportunity in the market, whether there is any anomaly in the market, whether the market is efficient, whether there is any preference of any higher-order moment in the market, and whether there is any higher-order Stochastic Dominance in the market. Thus, our findings enable academics and practitioners to draw better decision in their analysis.
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Central Moments, Stochastic Dominance and Expected Utility
SSRN Electronic Journal, 2016Co-Authors: Raymond H. Chan, Sheung-chi Chow, Wing-keung WongAbstract:In this paper, we develop some theories related to relationships between central moments, Stochastic Dominance (SD) and expected utility. The first part of our discussion focus on the relationship between central moments, different order integrals and Stochastic Dominance as well as relationship between central moments, different order reversed integrals and risk seeking Stochastic Dominance. The second part of our discussion focus on the relationship between central moments and different form of expected utility. Part of our results could be viewed as a generalization of theorems in Chan, et al. (2012). The results in our paper can be used to develop the relationship between moments and prospect SD (PSD) and Markowitz SD (MSD).
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A Note on Stochastic Dominance and the Omega Ratio
SSRN Electronic Journal, 2016Co-Authors: Xu Guo, Xuejun Jiang, Wing-keung WongAbstract:We first show that second-order Stochastic Dominance (SSD) and/or second-order risk-seeking Stochastic Dominance (SRSD) alone for any two prospects is not sufficient to imply the Omega ratio of one asset is always greater than that of the other one. We then extend the theory of risk measures by proving that the preference of second-order Stochastic Dominance implies the preference of the corresponding Omega ratios only when the return threshold is less than the mean of the higher-return asset. On the other hand, the preference of second-order risk-seeking Stochastic Dominance implies the preference of the corresponding Omega ratios only when the return threshold is bigger than the mean of the smaller-return asset. Nonetheless, the preference of first-order Stochastic Dominance does imply the preference of the corresponding Omega ratios for any return threshold.
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A Note on Almost Stochastic Dominance
2013Co-Authors: Xu Guo, Xuehu Zhu, Wing-keung Wong, Lixing ZhuAbstract:To satisfy the property of expected-utility maximization, Tzeng et al. (2012) modify the almost second-degree Stochastic Dominance proposed by Leshno and Levy (2002) and define almost higher-degree Stochastic Dominance. In this note, we further investigate the relevant properties. We define an almost third-degree Stochastic Dominance in the same way that Leshno and Levy (2002) define second-degree Stochastic Dominance and show that Leshno and Levy's (2002) almost Stochastic Dominance has the hierarchy property but not expected-utility maximization. In contrast, Tzeng et al.'s (2012) definition has the property of expected-utility maximization but not the hierarchy property. This phenomenon also holds for higher-degree Stochastic Dominance for these two concepts. Thus, the findings in this paper suggest that Leshno and Levy's (2002) definitions of ASSD and ATSD might be better than those defined by Tzeng et al. (2012) if the hierarchy property is considered to be an important issue.
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Moment Conditions for Almost Stochastic Dominance
SSRN Electronic Journal, 2013Co-Authors: Xu Guo, Wing-keung Wong, Thierry Post, Lixing ZhuAbstract:In this paper we �first develop a theory of almost Stochastic Dominance for risk-seeking investors to the first three orders. Thereafter, we study the relationship between the preferences of almost Stochastic Dominance for risk-seekers with that for risk averters.
Haim Levy - One of the best experts on this subject based on the ideXlab platform.
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Stochastic Dominance: The Quantile Approach
Stochastic Dominance, 2016Co-Authors: Haim LevyAbstract:In Chap. 3 the various Stochastic Dominance rules were stated in terms of cumulative distributions denoted by F and G. In this chapter FSD and SSD Stochastic Dominance are restated in terms of distribution quantiles. Both methods yield the same partition of the feasible set into efficient and inefficient sets. The formulas and the Stochastic Dominance rules based on distribution quantiles are more difficult to grasp intuitively but, as will be shown in this chapter, they are more easily extended to the case of diversification between risky asset and riskless assets. They are also more easily extended to the analysis of Stochastic Dominance among specific distributions of rates of return (e.g., lognormal distributions). Such extensions are quite difficult in the cumulative distribution framework.
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Stochastic Dominance investment decision making under uncertainty
2010Co-Authors: Haim LevyAbstract:Preface. 1. On the Measurement of Risk. 2. Expected Utility Theory. 3. Stochastic Dominance Decision Rules. 4. Stochastic Dominance: The Quantile Approach. 5. Algorithms for Stochastic Dominance. 6. Stochastic Dominance with Specific Distributions. 7. The Empirical Studies. 8. Applications of Stochastic Dominance Rules. 9. Stochastic Dominance and Risk Measures. 10. Stochastic Dominance and Diversification. 11. Decision Making and the Investment Horizon. 12. The CAPM and Stochastic Dominance. 13. Non-Expected Utility and Stochastic Dominance. 14. Future Research.
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Stochastic Dominance and Medical Decision Making
Health care management science, 2004Co-Authors: Moshe Leshno, Haim LevyAbstract:Stochastic Dominance (SD) criteria are decision making tools which allow us to choose among various strategies with only partial information on the decision makers' preferences. The notion of Stochastic Dominance has been extensively employed and developed in the area of economics, finance, agriculture, statistics, marketing and operation research since the late 1960s. For example, it may tell us which of two medical treatments with uncertain outcomes is preferred in the absence of full information on the patients' preferences. This paper presents a short review of the SD paradigm and demonstrates how the SD criteria may be employed in medical decision making, using the case of small abdominal aortic aneurysms as an illustration. Thus, for instance by assuming risk aversion one can employ second-degree Stochastic Dominance to divide the set of all possible treatments into the efficient set, from which the decision makers should always choose, and the inefficient (inferior) set. By employing Prospect Stochastic Dominance (PSD) a similar division can be conducted corresponding to all S-shaped utility functions.
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Stochastic Dominance: The Quantile
Studies in Risk and Uncertainty, 1998Co-Authors: Haim LevyAbstract:In Chapter 3 the various Stochastic Dominance rules were stated in terms of cumulative distributions denoted by F and G. In this chapter FSD, SSD, TSD, and nth order Stochastic Dominance are restated in terms of distribution quantiles. Both methods yield the same partition of the feasible set into efficient and inefficient sets. The formulas and the Stochastic Dominance rules based on distribution quantiles are more difficult to grasp intuitively but, as will be shown in this chapter, they are more easily extended to the case of diversification between risky asset and riskless assets. They are also more easily extended to the analysis of Stochastic Dominance among specific distributions of rates of return (e.g., lognormal distributions). Such extensions are quite difficult in the cumulative distribution framework.
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Stochastic Dominance and expected utility survey and analysis
Management Science, 1992Co-Authors: Haim LevyAbstract: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.
Xu Guo - One of the best experts on this subject based on the ideXlab platform.
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farinelli and tibiletti ratio and Stochastic Dominance
Risk Management, 2019Co-Authors: Xu Guo, Cuizhen Niu, Wing-keung WongAbstract:Farinelli and Tibiletti (F–T) ratio, a general risk-reward performance measurement ratio, is popular due to its simplicity and yet generality that both Omega ratio and upside potential ratio are its special cases. The F–T ratios are ratios of average gains to average losses with respect to a target, each raised by a power index, p and q. In this paper, we establish the consistency of F–T ratios with any nonnegative values p and q with respect to first-order Stochastic Dominance. Second-order Stochastic Dominance does not lead to F–T ratios with any nonnegative values p and q, but can lead to F–T Dominance with any $$p<1$$ and $$q\ge 1$$ . Furthermore, higher-order Stochastic Dominance ( $$n\ge 3$$ ) leads to F–T Dominance with any $$p<1$$ and $$q\ge n-1$$ . We also find that when the variables being compared belong to the same location-scale family or the same linear combination of location-scale families, we can get the necessary relationship between the Stochastic Dominance with the F–T ratio after imposing some conditions on the means. There are many advantages of using the F–T ratio over other measures, and academics and practitioners can benefit by using the theory we developed in this paper. For example, the F–T ratio can be used to detect whether there is any arbitrage opportunity in the market, whether there is any anomaly in the market, whether the market is efficient, whether there is any preference of any higher-order moment in the market, and whether there is any higher-order Stochastic Dominance in the market. Thus, our findings enable academics and practitioners to draw better decision in their analysis.
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A Note on Stochastic Dominance and the Omega Ratio
SSRN Electronic Journal, 2016Co-Authors: Xu Guo, Xuejun Jiang, Wing-keung WongAbstract:We first show that second-order Stochastic Dominance (SSD) and/or second-order risk-seeking Stochastic Dominance (SRSD) alone for any two prospects is not sufficient to imply the Omega ratio of one asset is always greater than that of the other one. We then extend the theory of risk measures by proving that the preference of second-order Stochastic Dominance implies the preference of the corresponding Omega ratios only when the return threshold is less than the mean of the higher-return asset. On the other hand, the preference of second-order risk-seeking Stochastic Dominance implies the preference of the corresponding Omega ratios only when the return threshold is bigger than the mean of the smaller-return asset. Nonetheless, the preference of first-order Stochastic Dominance does imply the preference of the corresponding Omega ratios for any return threshold.
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A Note on Almost Stochastic Dominance
2013Co-Authors: Xu Guo, Xuehu Zhu, Wing-keung Wong, Lixing ZhuAbstract:To satisfy the property of expected-utility maximization, Tzeng et al. (2012) modify the almost second-degree Stochastic Dominance proposed by Leshno and Levy (2002) and define almost higher-degree Stochastic Dominance. In this note, we further investigate the relevant properties. We define an almost third-degree Stochastic Dominance in the same way that Leshno and Levy (2002) define second-degree Stochastic Dominance and show that Leshno and Levy's (2002) almost Stochastic Dominance has the hierarchy property but not expected-utility maximization. In contrast, Tzeng et al.'s (2012) definition has the property of expected-utility maximization but not the hierarchy property. This phenomenon also holds for higher-degree Stochastic Dominance for these two concepts. Thus, the findings in this paper suggest that Leshno and Levy's (2002) definitions of ASSD and ATSD might be better than those defined by Tzeng et al. (2012) if the hierarchy property is considered to be an important issue.
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Moment Conditions for Almost Stochastic Dominance
SSRN Electronic Journal, 2013Co-Authors: Xu Guo, Wing-keung Wong, Thierry Post, Lixing ZhuAbstract:In this paper we �first develop a theory of almost Stochastic Dominance for risk-seeking investors to the first three orders. Thereafter, we study the relationship between the preferences of almost Stochastic Dominance for risk-seekers with that for risk averters.
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A note on almost Stochastic Dominance
Economics Letters, 2013Co-Authors: Xu Guo, Xuehu Zhu, Wing-keung Wong, Lixing ZhuAbstract:Both the expected-utility maximization and the hierarchy property are very important properties in Stochastic Dominance. For almost Stochastic Dominance, Leshno and Levy (2002) propose a definition and Tzeng et al. (2013) modified it to give another definition. This note provides more information on the two definitions. The former has the hierarchy property but not the expected-utility maximization, whereas the latter has the expected-utility maximization but not the hierarchy property.
Andrzej Ruszczynski - One of the best experts on this subject based on the ideXlab platform.
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Tractable Almost Stochastic Dominance
European Journal of Operational Research, 2012Co-Authors: Andrey Lizyayev, Andrzej RuszczynskiAbstract:LL-Almost Stochastic Dominance (LL-ASD) is a relaxation of the Stochastic Dominance (SD) concept proposed by Leshno and Levy that explains more of realistic preferences observed in practice than SD alone does. Unfortunately, numerical applications of this concept, such as identifying if a given portfolio is efficient or determining a marketed portfolio that dominates a given benchmark, are computationally prohibitive due to the structure of LL-ASD. We propose a new Almost Stochastic Dominance (ASD) concept that is computationally tractable. For instance, a marketed dominating portfolio can be identified by solving a simple linear programming problem. Moreover, the new concept performs well on all the intuitive examples from the literature, and in some cases leads to more realistic predictions than the earlier concept. We develop some properties of ASD, formulate efficient optimization models, and apply the concept to analyzing investors’ preferences between bonds and stocks for the long run.
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Optimization Under First Order Stochastic Dominance Constraints
2005Co-Authors: Darinka Dentcheva, Andrzej RuszczynskiAbstract:We consider Stochastic optimization problems involving Stochastic Dominance constraints of first order, also called Stochastic ordering constraints. They are equivalent to a continuum of probabilistic constraints or chance constraints. We develop first order necessary and sufficient conditions of optimality for these models. We show that the Lagrange multipliers corresponding to Stochastic Dominance constraints are piecewise constant nondecreasing utility functions. These results extend our theory of Stochastic Dominance-constrained optimization to the first order case, in which the main challenge is the potential non- convexity of the problem. We also show that the convexification of Stochastic ordering relation is equivalent to second order Stochastic Dominance under rather weak assumptions. This paper appeared as "Semi-Infinite Probabilistic Optimization: First Order Stochastic Dominance Constraints" in "Optimization" 53(2004) 583-- 601.
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Dual Stochastic Dominance and Related Mean-Risk Models
SIAM Journal on Optimization, 2002Co-Authors: Włodzimierz Ogryczak, Andrzej RuszczynskiAbstract:We consider the problem of constructing mean-risk models which are consistent with the second degree Stochastic Dominance relation. By exploiting duality relations of convex analysis we develop the quantile model of Stochastic Dominance for general distributions. This allows us to show that several models using quantiles and tail characteristics of the distribution are in harmony with the Stochastic Dominance relation. We also provide Stochastic linear programming formulations of these models.
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On consistency of Stochastic Dominance and mean–semideviation models
Mathematical Programming, 2001Co-Authors: Włodzimierz Ogryczak, Andrzej RuszczynskiAbstract:We analyze relations between two methods frequently used for modeling the choice among uncertain outcomes: Stochastic Dominance and mean–risk approaches. New necessary conditions for Stochastic Dominance are developed. These conditions compare values of a certain functional, which contains two components: the expected value of a random outcome and a risk term represented by the central semideviation of the corresponding degree. If the weight of the semideviation in the composite objective does not exceed the weight of the expected value, maximization of such a functional yields solutions which are efficient in terms of Stochastic Dominance. The results are illustrated graphically.
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on consistency of Stochastic Dominance and mean semideviation models
Mathematical Programming, 2001Co-Authors: Włodzimierz Ogryczak, Andrzej RuszczynskiAbstract:We analyze relations between two methods frequently used for modeling the choice among uncertain outcomes: Stochastic Dominance and mean–risk approaches. New necessary conditions for Stochastic Dominance are developed. These conditions compare values of a certain functional, which contains two components: the expected value of a random outcome and a risk term represented by the central semideviation of the corresponding degree. If the weight of the semideviation in the composite objective does not exceed the weight of the expected value, maximization of such a functional yields solutions which are efficient in terms of Stochastic Dominance. The results are illustrated graphically.
Rachel J. Huang - One of the best experts on this subject based on the ideXlab platform.
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Operational asymptotic Stochastic Dominance
European Journal of Operational Research, 2020Co-Authors: Rachel J. Huang, Larry Y. Tzeng, Jr-yan Wang, Lin ZhaoAbstract:Abstract Levy (2016) proposes asymptotic first-degree Stochastic Dominance as a distribution ranking criterion for all non-satiable decision makers with infinite investment horizons. Given Levy’s setting, this paper defines and offers the equivalent distributional conditions for asymptotic second-degree Stochastic Dominance, as well as operational asymptotic first- and second-degree Stochastic Dominance. Interestingly, the operational asymptotic Stochastic Dominance provides a full rank over assets with lognormal returns and different means. Empirical applications show that our conditions can be readily implemented in practice.
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Fractional Degree Stochastic Dominance
Management Science, 2020Co-Authors: Rachel J. Huang, Larry Y. Tzeng, Lin ZhaoAbstract:We develop a continuum of Stochastic Dominance rules for expected utility maximizers. The new rules encompass the traditional integer-degree Stochastic Dominance; between adjacent integer degrees, ...
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Bivariate almost Stochastic Dominance
Economic Theory, 2014Co-Authors: Michel Denuit, Rachel J. Huang, Larry Y. TzengAbstract:Univariate almost Stochastic Dominance has been widely studied and applied since its introduction by Leshno and Levy (Manag Sci 48:1074–1085, 2002). This paper extends this construction to the bivariate case by means of suitable two-attribute utility functions. After having confined correlation aversion and correlation loving to some acceptable levels, bivariate almost Stochastic Dominance rules are introduced for the preferences exhibiting confined correlation aversion and confined correlation loving. The impact of a change in risk in terms of bivariate almost Stochastic Dominance on optimal saving is analyzed as an application, as well as the effect of envy and altruism on income distributions. Finally, alternative definitions of bivariate almost Stochastic Dominance are discussed, as well as testing procedures for such Dominance rules in financial problems.
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Bivariate almost Stochastic Dominance
2014Co-Authors: Michel Denuit, Rachel J. Huang, Larry Y. TzengAbstract:Univariate almost Stochastic Dominance has been widely studied and applied since its introduction by Leshno and Levy (Manag Sci 48:1074–1085, 2002 ). This paper extends this construction to the bivariate case by means of suitable two-attribute utility functions. After having confined correlation aversion and correlation loving to some acceptable levels, bivariate almost Stochastic Dominance rules are introduced for the preferences exhibiting confined correlation aversion and confined correlation loving. The impact of a change in risk in terms of bivariate almost Stochastic Dominance on optimal saving is analyzed as an application, as well as the effect of envy and altruism on income distributions. Finally, alternative definitions of bivariate almost Stochastic Dominance are discussed, as well as testing procedures for such Dominance rules in financial problems. Copyright Springer-Verlag Berlin Heidelberg 2014 (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.)
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Almost marginal conditional Stochastic Dominance
Journal of Banking & Finance, 2014Co-Authors: Michel Denuit, Rachel J. Huang, Larry Y. Tzeng, Christine W. WangAbstract:Marginal Conditional Stochastic Dominance (MCSD) developed by Shalit and Yitzhaki (1994) gives the conditions under which all risk-averse individuals prefer to increase the share of one risky asset over another in a given portfolio. In this paper, we extend this concept to provide conditions under which most (and not all) risk-averse investors behave in this way. Instead of Stochastic Dominance rules, almost Stochastic Dominance is used to assess the superiority of one asset over another in a given portfolio. Switching from MCSD to Almost MCSD (AMCSD) helps to reconcile common practices in asset allocation and the decision rules supporting Stochastic Dominance relations. A financial application is further provided to demonstrate that using AMCSD can indeed improve investment efficiency.
