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Almost first-order stochastic dominance by distorted expectations

Part of: Mathematical economics Distribution theory - Probability

Published online by Cambridge University Press:  12 August 2022

Jianping Yang ,
Tian Zhou  and
Weiwei Zhuang Open the ORCID record for Weiwei Zhuang [Opens in a new window]
Jianping Yang
Affiliation:
Department of Mathematical Sciences, School of Science, Zhejiang Sci-Tech University, Hangzhou, Zhejiang 310018, China. E-mails: yangjp@zstu.edu.cn; ztian980117@163.com
Tian Zhou
Affiliation:
Department of Mathematical Sciences, School of Science, Zhejiang Sci-Tech University, Hangzhou, Zhejiang 310018, China. E-mails: yangjp@zstu.edu.cn; ztian980117@163.com
Weiwei Zhuang
Affiliation:
International Institute of Finance, School of Management, University of Science and Technology of China, Hefei, Anhui 230026, China. E-mail: weizh@ustc.edu.cn
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Abstract

Almost stochastic dominance has been receiving a great amount of attention in the financial and economic literatures. In this paper, we characterize the properties of almost first-order stochastic dominance (AFSD) via distorted expectations and investigate the conditions under which AFSD is preserved under a distortion transform. The main results are also applied to establish stochastic comparisons of order statistics and receiver operating characteristic curves via AFSD.

Keywords

Almost first-order stochastic dominanceDecision analysisDistortion functionOrder statisticsROC curve

MSC classification

Primary: 60E15: Inequalities; stochastic orderings
Secondary: 91B16: Utility theory

Information

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 37 , Issue 4 , October 2023 , pp. 888 - 906
Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

Atkinson, A.B. (2008). More on the measurement of inequality. Journal of Economic Inequality 6(3): 277–283.CrossRefGoogle Scholar
Balbás, A., Garrido, J., & Mayoral, S. (2009). Properties of distortion risk measures. Methodology & Computing in Applied Probability 11(3): 385–399.CrossRefGoogle Scholar
Bali, T.G., Demirtas, K.O., Levy, H., & Wolf, A. (2009). Bonds versus stocks: Investors’ age and risk taking. Journal of Monetary Economics 56(6): 817–830.CrossRefGoogle Scholar
Boland, P.J., Hu, T., Shaked, M., & Shanthikumar, J.G. (2002). Stochastic ordering of order statistics II. In M. Dror, P. L'Ecuyer, & F. Szidarovszky (eds), Modeling uncertainty: An examination of stochastic theory, methods, and applications. Boston: Kluwer Academic Publishers, pp. 607–623.CrossRefGoogle Scholar
Denuit, M., Dhaene, J., Goovaerts, M., & Kaas, R. (2005). Actuarial theory for dependent risks: Measures, orders and models. West Sussex: John Wiley & Sons, Ltd.CrossRefGoogle Scholar
Donaldson, D. & Weymark, J.A. (1983). Ethically flexible Gini indices for income distributions in continuum. Journal of Economic Theory 29(2): 353–358.CrossRefGoogle Scholar
Fawcett, T. (2005). An introduction to ROC analysis. Pattern Recognition Letters 27(8): 861–874.CrossRefGoogle Scholar
Föllmer, H. & Schied, A (2016). Stochastic finance: An introduction in discrete time. 4th ed. Berlin: Walter de Gruyter.CrossRefGoogle Scholar
Gigliarano, C., Figini, S., & Muliere, P. (2014). Making classifier performance comparisons when ROC curves intersect. Computational Statistics and Data Analysis 77: 300–312.CrossRefGoogle Scholar
Guo, X., Zhu, X., Wong, W.-K., & Zhu, L. (2013). A note on almost stochastic dominance. Economics Letters 121: 252–256.CrossRefGoogle Scholar
Guo, X., Post, T., Wong, W.-K., & Zhu, L. (2014). Moment conditions for almost stochastic dominance. Economics Letters 124: 163–167.CrossRefGoogle Scholar
Guo, D., Hu, Y., Wang, S., & Zhao, L. (2016). Comparing risks with reference points: A stochastic dominance approach. Insurance: Mathematics and Economics 70: 105–116.Google Scholar
Hadar, J. & Russell, W. (1969). Rules for ordering uncertain prospects. American Economic Review 59: 25–34.Google Scholar
Hanoch, G. & Levy, H. (1969). The efficiency analysis of choice involving risk. The Review of Economic Studies 36(3): 335–346.CrossRefGoogle Scholar
Kirmani, S. & Gupta, R. (2001). On the proportional odds model in survival analysis. Annals of the Institute of Statistical Mathematics 53(2): 203–216.CrossRefGoogle Scholar
Lando, T., Arab, I., & Oliveira, P.E. (2021). Second-order stochastic comparisons of order statistics. Statistics 55(3): 561–579.CrossRefGoogle Scholar
Leshno, M. & Levy, H. (2002). Prefered by all and preferred by most decision makers: Almost stochastic dominance. Management Science 48: 1074–1085.CrossRefGoogle Scholar
Levy, M. (2012). Almost stochastic dominance and efficient investment sets. American Journal of Operations Research 2: 313–321.CrossRefGoogle Scholar
Levy, H. (2016). Stochastic dominance, 3rd ed. New York: Springer.CrossRefGoogle Scholar
Levy, H. & Wiener, Z. (1998). Stochastic dominance and prospect dominance with subjective weighting functions. Journal of Risk and Uncertainty 16(2): 147–163.CrossRefGoogle Scholar
Levy, H., Leshno, M., & Leibovitch, B. (2010). Economically relevant preferences for all observed epsilon. Annals of Operations Research 176: 153–178.CrossRefGoogle Scholar
Lusted, L. (1971). Signal detectability and medical decision-making. Science 171(3977): 1217–1219.CrossRefGoogle ScholarPubMed
Muliere, P. & Scarsini, M. (1989). A note on stochastic dominance and inequality measures. Journal of Economic Theory 49(2): 314–323.CrossRefGoogle Scholar
Müller, A. & Stoyan, D. (2002). Comparison methods for stochastic models and risks. Chichester, UK: John Wiley & Sons.Google Scholar
Müller, A., Scarsini, M., Tsetlin, I., & Winkler, R. (2017). Between first- and second-order stochatic dominance. Management Science 63: 2933–2974.CrossRefGoogle Scholar
Müller, A., Scarsini, M., Tsetlin, I., & Winkler, R. (2021). Ranking distributions when only means and variances are known. Operations Research. doi:10.1287/opre.2020.2072Google Scholar
Navarro, J., Ruiz, J.M., & Aguila, Y.D. (2008). Characterizations and ordering properties based on log-odds functions. Statistics 42(4): 313–328.CrossRefGoogle Scholar
Rothschild, M. & Stiglitz, J.E. (1970). Increasing risk: I. A definition. Journal of Economic Theory 2: 225–243.CrossRefGoogle Scholar
Sankaran, P.G. & Jayakumar, K. (2008). On proportional odds models. Statistical Papers 49(4): 779–789.CrossRefGoogle Scholar
Shaked, M. & Shanthikumar, J.G. (2007). Stochastic orders. New York: Springer.CrossRefGoogle Scholar
Tzeng, L.Y., Huang, R.J., & Shih, P.T. (2013). Revisiting almost second-degree stochastic dominance. Management Science 59: 1250–1254.CrossRefGoogle Scholar
Wang, S. (1995). Insurance pricing and increased limits ratemaking by propositional hazards transforms. Insurance: Mathematics and Economics 17: 43–54.Google Scholar
Wang, S. (2000). A class of distortion operators for pricing financial and insurance risk. Journal of Risk and Insurance 67: 15–36.CrossRefGoogle Scholar
Wang, S.S. & Young, V.R. (1998). Ordering risks: Expected utility theory versus Yaari's dual theory of risk. Insurance Mathematics and Economics 22(2): 145–161.CrossRefGoogle Scholar
Yaari, M.E. (1987). The dual theory of choice under risk. Economerica 9: 5–115.Google Scholar
Zimmer, W.J., Wang, Y., & Pathak, P.K. (1998). Log-odds rate and monotone log-odds rate distributions. Journal of Quality Technology 30(4): 376–385.CrossRefGoogle Scholar