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Measure of riskiness based on RDEU model

  • 1.

    School of Data Science, University of Science and Technology of China, Hefei 230026, China

  • 2.

    School of Management, University of Science and Technology of China, Hefei 230026, China

Cite this:
https://doi.org/10.52396/JUST-2021-0012
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  • Author Bio:

    Guo Chuanfeng is currently a graduate student under the tutelage of Prof. Mao Tiantian at University of Science and Technology of China. Her research interests focus on Risk measurement and practical application.

    Du Xinze received a bachelor's degree in statistics from the University of Science and Technology of China and continued his studies. He is now a PhD in Applied Mathematics from the University of Southern California.

    Wu Qinyu is a PhD candidate in the School of Management, University of Science and Technology of China, and his research direction is risk management and mathematical finance.

  • Corresponding author: Mao Tiantian (corresponding author) is an associate professor at University of Science and Technology of China (USTC). In 2012, she obtained PhD in Science from the University of Science and Technology of China. In May of the same year, she entered the Department of Statistics and Finance of the School of Management for postdoctoral work. Her research fields include risk measurement, risk management, random dominance and extreme value theory, etc. E-mail: tmao@ustc.edu.cn
  • Publish Date: 31 January 2021
    Abstract

  • Abstract

    Motivated by References[3,4], we introduce a new measure of riskiness based on the rank-dependent expected utility (RDEU) model. The new measure of riskiness is a generalized class of risk measures which includes the economic index of riskiness of Reference[3] and the operational measure of riskiness of Reference[4] as special cases. We probe into the basic properties as a measure of riskiness such as monotonicity, positive homogeneity and subadditivity. We study its applications in comparative risk aversion as well. In addition, we present a simulation to illustrate the results.

    Abstract

    Motivated by References[3,4], we introduce a new measure of riskiness based on the rank-dependent expected utility (RDEU) model. The new measure of riskiness is a generalized class of risk measures which includes the economic index of riskiness of Reference[3] and the operational measure of riskiness of Reference[4] as special cases. We probe into the basic properties as a measure of riskiness such as monotonicity, positive homogeneity and subadditivity. We study its applications in comparative risk aversion as well. In addition, we present a simulation to illustrate the results.
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    • References(16)
  • [1]
    Artzner P, Delbaen F, Eber J M, et al. Coherent measures of risk. Mathematical Finance, 1999, 9(3): 203-228.
    [2]
    Dowd K. Measuring Market Risk. Chichester: John Wiley & Sons, 2002.
    [3]
    Aumann R J, Serrano R. An economic index of riskiness. Journal of Political Economy, 2008, 116(5): 810-836.
    [4]
    Foster D P, Hart S. An operational measure of riskiness. Journal of Political Economy, 2009, 117(5): 785-814.
    [5]
    Quiggin J. A theory of anticipated utility. Journal of Economic Behavior & Organization, 1982, 3(4): 323-343.
    [6]
    Yaari M E. The dual theory of choice under risk. Econometrica, 1987, 55: 95-115.
    [7]
    Mao T, Cai J. Risk measures based on behavioural economics theory. Finance and Stochastics, 2018, 22(2): 367-393.
    [8]
    Diecidue E, Wakker P P. On the intuition of rank-dependent utility. Journal of Risk and Uncertainty, 2001, 23(3): 281-298.
    [9]
    Merkle M, Marinescu D, Merkle M M R, et al. Lebegue-Stieljes integral and Young's inequality. Applicable Analysis and Discrete Mathematics, 2014, 8: 60-72.
    [10]
    Wang S. Insurance pricing and increased limits ratemaking by proportional hazards transforms. Insurance: Mathematics and Economics, 1995, 17(1): 43-54.
    [11]
    Wang S. Premium calculation by transforming the layer premium density. ASTIN Bulletin, 1996, 26: 71-92.
    [12]
    Wang S. A class of distortion operators for pricing financial and insurance risks. Journal of Risk and Insurance, 2000, 67: 15-36.
    [13]
    Caballe J, Esteban J. Stochastic dominance and absolute risk aversion. Social Choice and Welfare, 2007, 28(1): 89-110.
    [14]
    Embrechts P, Wang R. Seven proofs for the subadditivity of expected shortfall. Dependence Modeling, 2015, 3(1): 126-140.
    [15]
    Wirch J L, Hardy M R. Distortion risk measures. coherence and stochastic dominance. Insurance Mathematics and Economics, 2001, 32(1): 168-168.
    [16]
    Riedel F. Dynamic coherent risk measures. Stochastic Processes and their Applications, 2004, 112(22): 185-200.
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    [1]
    Artzner P, Delbaen F, Eber J M, et al. Coherent measures of risk. Mathematical Finance, 1999, 9(3): 203-228.
    [2]
    Dowd K. Measuring Market Risk. Chichester: John Wiley & Sons, 2002.
    [3]
    Aumann R J, Serrano R. An economic index of riskiness. Journal of Political Economy, 2008, 116(5): 810-836.
    [4]
    Foster D P, Hart S. An operational measure of riskiness. Journal of Political Economy, 2009, 117(5): 785-814.
    [5]
    Quiggin J. A theory of anticipated utility. Journal of Economic Behavior & Organization, 1982, 3(4): 323-343.
    [6]
    Yaari M E. The dual theory of choice under risk. Econometrica, 1987, 55: 95-115.
    [7]
    Mao T, Cai J. Risk measures based on behavioural economics theory. Finance and Stochastics, 2018, 22(2): 367-393.
    [8]
    Diecidue E, Wakker P P. On the intuition of rank-dependent utility. Journal of Risk and Uncertainty, 2001, 23(3): 281-298.
    [9]
    Merkle M, Marinescu D, Merkle M M R, et al. Lebegue-Stieljes integral and Young's inequality. Applicable Analysis and Discrete Mathematics, 2014, 8: 60-72.
    [10]
    Wang S. Insurance pricing and increased limits ratemaking by proportional hazards transforms. Insurance: Mathematics and Economics, 1995, 17(1): 43-54.
    [11]
    Wang S. Premium calculation by transforming the layer premium density. ASTIN Bulletin, 1996, 26: 71-92.
    [12]
    Wang S. A class of distortion operators for pricing financial and insurance risks. Journal of Risk and Insurance, 2000, 67: 15-36.
    [13]
    Caballe J, Esteban J. Stochastic dominance and absolute risk aversion. Social Choice and Welfare, 2007, 28(1): 89-110.
    [14]
    Embrechts P, Wang R. Seven proofs for the subadditivity of expected shortfall. Dependence Modeling, 2015, 3(1): 126-140.
    [15]
    Wirch J L, Hardy M R. Distortion risk measures. coherence and stochastic dominance. Insurance Mathematics and Economics, 2001, 32(1): 168-168.
    [16]
    Riedel F. Dynamic coherent risk measures. Stochastic Processes and their Applications, 2004, 112(22): 185-200.
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