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The bounds of premium and optimality of stop loss insurance under uncertain random environments

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  • Liu, Ying
  • Li, Xiaozhong
  • Liu, Yinli

Abstract

The potential loss of insured can be affected by many nondeterministic factors, in which uncertainty always coexists with randomness. Therefore, uncertain random variables are used to describe this phenomenon of simultaneous appearance of both uncertainty and randomness in potential loss. Based on that, the upper and lower bounds of premium with uncertain random loss are given, respectively. Moreover, a mathematical model of uncertain random optimal insurance problem is established and the stop loss insurance is proved to be the optimal insurance policy and the equation for calculating the optimal deductible is arrived. Some numerical examples are also given for illustration.

Suggested Citation

  • Liu, Ying & Li, Xiaozhong & Liu, Yinli, 2015. "The bounds of premium and optimality of stop loss insurance under uncertain random environments," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 273-278.
    • Handle: RePEc:eee:insuma:v:64:y:2015:i:c:p:273-278
    DOI: 10.1016/j.insmatheco.2015.06.004
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    References listed on IDEAS

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    1. Lu, ZhiYi & Liu, LePing & Zhang, JianYu & Meng, LiLi, 2012. "Optimal insurance under multiple sources of risk with positive dependence," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 462-471.
    2. J. David Cummins & Richard Derrig, 1997. "Fuzzy Financial Pricing of Property-Liability Insurance," North American Actuarial Journal, Taylor & Francis Journals, vol. 1(4), pages 21-40.
    3. Zou, Bin & Cadenillas, Abel, 2014. "Optimal investment and risk control policies for an insurer: Expected utility maximization," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 57-67.
    4. Gur Huberman & David Mayers & Clifford W. Smith Jr., 1983. "Optimal Insurance Policy Indemnity Schedules," Bell Journal of Economics, The RAND Corporation, vol. 14(2), pages 415-426, Autumn.
    5. Zhou, Chunyang & Wu, Wenfeng & Wu, Chongfeng, 2010. "Optimal insurance in the presence of insurer's loss limit," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 300-307, April.
    6. Rob Kaas & Marc Goovaerts & Jan Dhaene & Michel Denuit, 2008. "Modern Actuarial Risk Theory," Springer Books, Springer, edition 2, number 978-3-540-70998-5, December.
    7. Zhou, Chunyang & Wu, Chongfeng, 2008. "Optimal insurance under the insurer's risk constraint," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 992-999, June.
    8. Golubin, A.Y., 2008. "Optimal Insurance and Reinsurance Policies in the Risk Process," ASTIN Bulletin, Cambridge University Press, vol. 38(2), pages 383-397, November.
    9. Shapiro, Arnold F., 2004. "Fuzzy logic in insurance," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 399-424, October.
    10. Pliska, Stanley R. & Ye, Jinchun, 2007. "Optimal life insurance purchase and consumption/investment under uncertain lifetime," Journal of Banking & Finance, Elsevier, vol. 31(5), pages 1307-1319, May.
    11. Raviv, Artur, 1979. "The Design of an Optimal Insurance Policy," American Economic Review, American Economic Association, vol. 69(1), pages 84-96, March.
    12. Chavas, Jean-Paul, 2004. "Risk Analysis in Theory and Practice," Elsevier Monographs, Elsevier, edition 1, number 9780121706210.
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    2. 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.

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