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Log-supermodularity of weight functions, ordering weighted losses, and the loading monotonicity of weighted premiums

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  • Sendov, Hristo S.
  • Wang, Ying
  • Zitikis, Ricardas

Abstract

The paper is motivated by a problem concerning the monotonicity of insurance premiums with respect to their loading parameter: the larger the parameter, the larger the insurance premium is expected to be. This property, usually called the loading monotonicity, is satisfied by premiums that appear in the literature. The increased interest in constructing new insurance premiums has raised a question as to what weight functions would produce loading-monotonic premiums. In this paper, we demonstrate a decisive role of log-supermodularity or, equivalently, of total positivity of order 2 (TP2) in answering this question. As a consequence, we establish-at a stroke-the loading monotonicity of a number of well-known insurance premiums, and offer a host of further weight functions, and consequently of premiums, thus illustrating the power of the herein suggested methodology for constructing loading-monotonic insurance premiums.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:48:y:2011:i:2:p:257-264
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    References listed on IDEAS

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    1. Furman, Edward & Zitikis, Ricardas, 2008. "Weighted premium calculation principles," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 459-465, February.
    2. Jones, Bruce L. & Zitikis, Ricardas, 2007. "Risk measures, distortion parameters, and their empirical estimation," Insurance: Mathematics and Economics, Elsevier, vol. 41(2), pages 279-297, September.
    3. Broll, Udo & Egozcue, Martín & Wong, Wing-Keung & Zitikis, Ričardas, 2010. "Prospect theory and hedging risks," Dresden Discussion Paper Series in Economics 05/10, Technische Universität Dresden, Faculty of Business and Economics, Department of Economics.
    4. Donald M. Topkis, 1978. "Minimizing a Submodular Function on a Lattice," Operations Research, INFORMS, vol. 26(2), pages 305-321, April.
    5. Edward Furman & Ričardas Zitikis, 2009. "Weighted Pricing Functionals With Applications to Insurance," North American Actuarial Journal, Taylor & Francis Journals, vol. 13(4), pages 483-496.
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