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On the flexibility and loading maximization for weighted premiums

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  • Psarrakos, Georgios
  • Vliora, Polyxeni

Abstract

The premium principle is a rule of pricing that adjusts premium with insurance risk and is the core of stating actuary insurance. This paper deals with a class of weighted premium principles that uses a positive parameter to add flexibility for an actuary to control the degree of risk aversion, and complements the study of flexibility on the modified variance premium initiated in Goovaerts et al. [9]. We apply our approach for some well-known premium principles, studying some theoretical properties, and we establish the nonmonotonic unimodal premium principles with respect to the loading parameter. Therefore, we obtain a loading maximization of weighted premiums, a useful tool to feasible contracts. We illustrate the results by some numerical examples.

Suggested Citation

  • Psarrakos, Georgios & Vliora, Polyxeni, 2024. "On the flexibility and loading maximization for weighted premiums," Applied Mathematics and Computation, Elsevier, vol. 481(C).
    • Handle: RePEc:eee:apmaco:v:481:y:2024:i:c:s0096300324004053
    DOI: 10.1016/j.amc.2024.128944
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    References listed on IDEAS

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    1. Sendov, Hristo S. & Wang, Ying & Zitikis, Ricardas, 2011. "Log-supermodularity of weight functions, ordering weighted losses, and the loading monotonicity of weighted premiums," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 257-264, March.
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    3. Udo Kamps, 1998. "On a class of premium principles including the Esscher principle," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 1998(1), pages 75-80.
    4. Dickson,David C. M., 2005. "Insurance Risk and Ruin," Cambridge Books, Cambridge University Press, number 9780521846400.
    5. Bartoszewicz, Jaroslaw, 2009. "On a representation of weighted distributions," Statistics & Probability Letters, Elsevier, vol. 79(15), pages 1690-1694, August.
    6. Paul Embrechts, 2000. "Actuarial versus Financial Pricing of Insurance," Journal of Risk Finance, Emerald Group Publishing Limited, vol. 1(4), pages 17-26, March.
    7. Heilmann, Wolf-Rudiger, 1989. "Decision theoretic foundations of credibility theory," Insurance: Mathematics and Economics, Elsevier, vol. 8(1), pages 77-95, March.
    8. Asimit, Alexandru V. & Bignozzi, Valeria & Cheung, Ka Chun & Hu, Junlei & Kim, Eun-Seok, 2017. "Robust and Pareto optimality of insurance contracts," European Journal of Operational Research, Elsevier, vol. 262(2), pages 720-732.
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