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The uncertain premium principle based on the distortion function

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  • Li, Shengguo
  • Peng, Jin
  • Zhang, Bo

Abstract

In this paper, we discuss the premium principle in uncertain environment. First, the net premium principle for uncertain risks is presented within the framework of uncertainty theory. With the help of distortion function, a new uncertain premium principle is derived from the uncertain net premium. Some properties of uncertain distortion premium principle are proved. Furthermore, a sufficient and necessary condition that an uncertain premium principle is an uncertain distortion premium principle has been characterized. Finally, some examples are given to illustrate the calculations of the uncertain distortion premium.

Suggested Citation

  • Li, Shengguo & Peng, Jin & Zhang, Bo, 2013. "The uncertain premium principle based on the distortion function," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 317-324.
    • Handle: RePEc:eee:insuma:v:53:y:2013:i:2:p:317-324
    DOI: 10.1016/j.insmatheco.2013.06.005
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    References listed on IDEAS

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    8. Wu, Xianyi & Zhou, Xian, 2006. "A new characterization of distortion premiums via countable additivity for comonotonic risks," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 324-334, April.
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    Cited by:

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    2. Rashed Khanjani Shiraz & Madjid Tavana & Debora Di Caprio & Hirofumi Fukuyama, 2016. "Solving Geometric Programming Problems with Normal, Linear and Zigzag Uncertainty Distributions," Journal of Optimization Theory and Applications, Springer, vol. 170(3), pages 1075-1078, September.
    3. Qin, Zhongfeng, 2015. "Mean-variance model for portfolio optimization problem in the simultaneous presence of random and uncertain returns," European Journal of Operational Research, Elsevier, vol. 245(2), pages 480-488.
    4. Wasim Akram Mandal & Sahidul Islam, 2017. "Multiobjective geometric programming problem under uncertainty," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 27(4), pages 85-109.
    5. Lin Chen & Jin Peng & Bo Zhang & Isnaini Rosyida, 2017. "Diversified models for portfolio selection based on uncertain semivariance," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(3), pages 637-648, February.
    6. Wasim Akram Mandal, 2021. "Weighted Tchebycheff Optimization Technique Under Uncertainty," Annals of Data Science, Springer, vol. 8(4), pages 709-731, December.
    7. Yao, Kai & Qin, Zhongfeng, 2015. "A modified insurance risk process with uncertainty," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 227-233.
    8. Rashed Khanjani Shiraz & Madjid Tavana & Debora Di Caprio & Hirofumi Fukuyama, 2016. "Solving Geometric Programming Problems with Normal, Linear and Zigzag Uncertainty Distributions," Journal of Optimization Theory and Applications, Springer, vol. 170(1), pages 243-265, July.

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