Generalized Almost Stochastic Dominance

Tsetlin, Ilia; Winkler, Robert L.; Huang, Rachel J.; Tzeng, Larry Y.

doi:10.1287/opre.2014.1340

Cited by 75 publications

(36 citation statements)

References 16 publications

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“…It should be pointed out that as a partial order relation, the SD approach is not useful to rank all the random variables. However, as a screening device, the SD approach can divide the whole decision making set into an efficient subset and an inefficient one, and then the decision maker choose within the efficient former (See, e.g., Li 2009;Blavaskyy, 2010Blavaskyy, , 2011Tzeng et al,2013;Loomes et al, 2014;Tsetlin et al, 2015). Such statements are also suitable to our new SD criteria.…”

Section: Comparison Of the New Sd Criteria And The Classical Sd Rulesmentioning

confidence: 99%

“…Well-known specifications of SD are first degree SD (FSD) and second degree SD (SSD), which by far attract most of the attention in SD research. Due to the advantage mentioned above, the SD approach has been proved to be a powerful tool for ranking random variables and employed in various areas of finance, decision analysis, economics and statistics (See e.g., Meyer, 1989;Levy, 1992Levy, , 2006Chiu, 2005;Li, 2009;Blavaskyy, 2010Blavaskyy, , 2011Deutsch and Silber, 2011;Bibi, Duclos and Audrey, 2012; Yalonetzky, 2012;Tzeng et al, 2013;Loomes et al, 2014;Valentini, 2015;Tsetlin et al, 2015). Unfortunately, the SD approach is inefficient to rank transformations on random variables because it relies on the cumulative distribution functions (CDFs) of random variables, which are hard to calculate.…”

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A New Approach of Stochastic Dominance for Ranking Transformations on the Discrete Random Variable

Gao

Zhao

2017

Economics

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This paper presents some new stochastic dominance (SD) criteria for ranking transformations on a random variable, which is the first time that this is done for transformations under the discrete framework. By using the expected utility theory, the authors first propose a sufficient condition for general transformations by first degree SD (FSD), and further develop it into the necessary and sufficient condition for monotonic transformations. For the second degree SD (SSD) case, they divide the monotonic transformations into increasing and decreasing categories, and further derive their necessary and sufficient conditions, respectively. For two different discrete random variables with the same possible states, the authors obtain the sufficient and necessary conditions for FSD and SSD, respectively. The new SD criteria have the following features: each FSD condition is represented by the transformation functions and each SSD condition is characterized by the transformation functions and the probability distributions of the random variable. This is different from the classical SD approach where FSD and SSD conditions are described by cumulative distribution functions. Finally, a numerical example is provided to show the effectiveness of the new SD criteria. JEL C51 D81Keywords Stochastic dominance; transformation; utility theory; insurance AuthorsJianwei Gao, School of Economics and Management, North China Electric Power University, Beijing, China, gaojianwei111@sina.com Feng Zhao, School of Economics and Management, North China Electric Power University, Beijing, China Citation Jianwei Gao and Feng Zhao (2017). A New Approach of Stochastic Dominance for Ranking Transformations on the Discrete Random Variable. Economics: The Open-Access, Open-Assessment E-Journal, 11 (2017-14): 1-23. http:// dx.doi.org/10.5018/economics-ejournal.ja. Economics: The Open-Access, Open-Assessment E-Journal 11 (2017-14) www.economics-ejournal.org 2 IntroductionIn real world, many human activities in insurance and financial fields induce risk transformations. For example, we assume that an investor owns a house where X denotes the value of the house (a random variable). The investor can insure the house with various levels of deductions. By choosing two different deduction policies, the investor creates different transformations ( ) m X and ( ) n X . Then an interesting question occurs: which deduction policy (transformation) dominates the other? In other words, how to find an effective approach for ranking these transformations so as to choose the beneficial one? Stochastic dominance (SD) is one of the most famous approaches to comparing pairs of prospects. Presented in the context of expected utility theory, the SD approach has the advantage that it requires no restrictions on probability distributions. Well-known specifications of SD are first degree SD (FSD) and second degree SD (SSD), which by far attract most of the attention in SD research. Due to the advantage mentioned above, the SD approach has been proved to be a po...

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Section: Comparison Of the New Sd Criteria And The Classical Sd Rulesmentioning

confidence: 99%

mentioning

confidence: 99%

A New Approach of Stochastic Dominance for Ranking Transformations on the Discrete Random Variable

Gao

Zhao

2017

Economics

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“…Fong, Wong, and Lean [58][59][60][61][62] apply the SD test to examine the momentum effect in stock returns. They find that winner portfolios stochastically dominate loser portfolios at the second and third orders.…”

Section: Empirical Studiesmentioning

confidence: 99%

Management Science, Economics and Finance: A Connection

Chang¹,

McAleer²

2016

Int J Econ Manag Sci

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“…(see Levy, 1992Levy, , 2006Chakravarty and Zoli, 2012;Jouini et al, 2013;Tsetlin et al, 2015;Post et al, 2015 andPost, 2016; Gao and Zhao, 2017). The SD rules indicate when one random variable is to be ranked higher than another by specifying a condition which the difference between their cumulative distribution functions (CDFs) must satisfy.…”

Section: Introductionmentioning

confidence: 99%

Sufficient conditions of stochastic dominance for general transformations and its application in option strategy

Gao

Zhao

2018

Economics

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A counterexample is presented to show that the sufficient condition for one transformation dominating another by the second degree stochastic dominance, proposed by Theorem 5 of Levy (Stochastic dominance and expected utility: Survey and analysis, 1992), does not hold. Then, by restricting the monotone property of the dominating transformation, a revised exact sufficient condition for one transformation dominating another is given. Next, the stochastic dominance criteria, proposed by Meyer (Stochastic dominance and transformations of random variables, 1989) and developed by Levy (1992), are extended to the most general transformations. Moreover, such criteria are further generalized to transformations on discrete random variables. Finally, the authors employ this method to analyze the transformations resulting from holding a stock with the corresponding call option. JEL C51 D81Keywords Stochastic dominance; transformation; utility theory; option strategy Authors Jianwei Gao, School of Economics and Management, North China Electric Power University, Beijing, China Feng Zhao, School of Economics and Management, North China Electric Power University, Beijing, China, Yundong Gu, School of Mathematics and Physics, North China Electric Power University, Beijing, China Citation Jianwei Gao, Feng Zhao, and Yundong Gu (2018). Sufficient conditions of stochastic dominance for general transformations and its application in option strategy. Economics: The Open-Access, Open-Assessment E-Journal, 12 (2018- Economics: The Open-Access, Open-Assessment E-Journal 12 (2018-1) www.economics-ejournal.org 2 IntroductionStochastic dominance (SD) has been proved to be a powerful tool for ranking random variables and is employed in various fields such as finance, decision analysis, economics and statistics etc. (see Levy, 1992Levy, , 2006Chakravarty and Zoli, 2012;Jouini et al., 2013;Tsetlin et al., 2015;Post et al., 2015 andPost, 2016; Gao and Zhao, 2017). The SD rules indicate when one random variable is to be ranked higher than another by specifying a condition which the difference between their cumulative distribution functions (CDFs) must satisfy. However, economic and financial activities usually induce transformations of an initial risk, and the classical SD rules are inefficient in ranking such transformations. Transformations of random variables have been discussed in the early stochastic dominance literature, especially in the risk analysis portion. For example, Sandmo (1971) has used a particular linear, risk altering, transformation in discussing the comparative statics of risk. Russell (1971, 1974) have dealt with special cases of the transformation question, emphasizing its use in dealing with portfolios of random variables. Cheng et al. (1987) have used the transformation approach to address the comparative statics of first degree stochastic dominance shifts in a random variable within a general decision model context. Meyer (1989) has proposed the first and second stochastic dominance (FSD and SSD) criteria...

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Generalized Almost Stochastic Dominance

Cited by 75 publications

References 16 publications

A New Approach of Stochastic Dominance for Ranking Transformations on the Discrete Random Variable

A New Approach of Stochastic Dominance for Ranking Transformations on the Discrete Random Variable

Management Science, Economics and Finance: A Connection

Sufficient conditions of stochastic dominance for general transformations and its application in option strategy

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