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Risk measures based on behavioural economics theory

Author

Listed:
  • Tiantian Mao

    (University of Science and Technology of China)

  • Jun Cai

    (University of Waterloo)

Abstract

Coherent risk measures (Artzner et al. in Math. Finance 9:203–228, 1999) and convex risk measures (Föllmer and Schied in Finance Stoch. 6:429–447, 2002) are characterized by desired axioms for risk measures. However, concrete or practical risk measures could be proposed from different perspectives. In this paper, we propose new risk measures based on behavioural economics theory. We use rank-dependent expected utility (RDEU) theory to formulate an objective function and propose the smallest solution that minimizes the objective function as a risk measure. We also employ cumulative prospect theory (CPT) to introduce a set of acceptable regulatory capitals and define the infimum of the set as a risk measure. We show that the classes of risk measures derived from RDEU theory and CPT are equivalent, and they are all monetary risk measures. We present the properties of the proposed risk measures and give sufficient and necessary conditions for them to be coherent and convex, respectively. The risk measures based on these behavioural economics theories not only cover important risk measures such as distortion risk measures, expectiles and shortfall risk measures, but also produce new interesting coherent risk measures and convex, but not coherent risk measures.

Suggested Citation

  • Tiantian Mao & Jun Cai, 2018. "Risk measures based on behavioural economics theory," Finance and Stochastics, Springer, vol. 22(2), pages 367-393, April.
    • Handle: RePEc:spr:finsto:v:22:y:2018:i:2:d:10.1007_s00780-018-0358-6
    DOI: 10.1007/s00780-018-0358-6
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    Cited by:

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    2. Mao, Tiantian & Stupfler, Gilles & Yang, Fan, 2023. "Asymptotic properties of generalized shortfall risk measures for heavy-tailed risks," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 173-192.
    3. Elroi Hadad & Tomer Shushi & Rami Yosef, 2023. "Measuring Systemic Governmental Reinsurance Risks of Extreme Risk Events," Risks, MDPI, vol. 11(3), pages 1-11, February.
    4. Weiwei Li & Dejian Tian, 2023. "Robust optimized certainty equivalents and quantiles for loss positions with distribution uncertainty," Papers 2304.04396, arXiv.org.
    5. Zongxia Liang & Jianming Xia & Keyu Zhang, 2023. "Equilibrium stochastic control with implicitly defined objective functions," Papers 2312.15173, arXiv.org, revised Dec 2023.
    6. Cai, Jun & Wang, Ying, 2021. "Optimal capital allocation principles considering capital shortfall and surplus risks in a hierarchical corporate structure," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 329-349.
    7. Chen, Ouxiang & Hu, Taizhong, 2019. "Extreme-aggregation measures in the RDEU model," Statistics & Probability Letters, Elsevier, vol. 148(C), pages 155-163.
    8. Mao, Tiantian & Hu, Jiuyun & Liu, Haiyan, 2018. "The average risk sharing problem under risk measure and expected utility theory," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 170-179.
    9. Ruoxuan Li & Wenhua Lv & Tiantian Mao, 2023. "Shortfall-Based Wasserstein Distributionally Robust Optimization," Mathematics, MDPI, vol. 11(4), pages 1-25, February.
    10. René Carmona, 2022. "The influence of economic research on financial mathematics: Evidence from the last 25 years," Finance and Stochastics, Springer, vol. 26(1), pages 85-101, January.
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    12. Qinyu Wu & Fan Yang & Ping Zhang, 2023. "Conditional generalized quantiles based on expected utility model and equivalent characterization of properties," Papers 2301.12420, arXiv.org.

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    More about this item

    Keywords

    Distortion risk measure; Expectile; Coherent risk measure; Convex risk measure; Monetary risk measure; Stop-loss order preserving; Rank-dependent expected utility theory; Cumulative prospect theory;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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