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Optimal Pricing of a Heterogeneous Portfolio for a Given Risk Level

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  • Zaks, Yaniv
  • Frostig, Esther
  • Levikson, Benny

Abstract

Consider a portfolio containing heterogeneous risks, where the policyholders’ premiums to the insurance company might not cover the claim payments. This risk has to be taken into consideration in the premium pricing. On the other hand, the premium that the insureds pay has to be fair. This fairness is measured by the distance between the risk and the premium paid. We apply a non-linear programming formulation to find the optimal premium for each class so that the risk is below a given level and the weighted distance between the risk and the premium is minimized. We consider also the dual problem: minimizing the risk level for a given weighted distance between risks and premium.

Suggested Citation

  • Zaks, Yaniv & Frostig, Esther & Levikson, Benny, 2006. "Optimal Pricing of a Heterogeneous Portfolio for a Given Risk Level," ASTIN Bulletin, Cambridge University Press, vol. 36(1), pages 161-185, May.
    • Handle: RePEc:cup:astinb:v:36:y:2006:i:01:p:161-185_01
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    Citations

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    Cited by:

    1. Righi, Marcelo Brutti & Müller, Fernanda Maria & Moresco, Marlon Ruoso, 2020. "On a robust risk measurement approach for capital determination errors minimization," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 199-211.
    2. Jaume Belles-Sampera & Montserrat Guillen & Miguel Santolino, 2023. "Haircut Capital Allocation as the Solution of a Quadratic Optimisation Problem," Mathematics, MDPI, vol. 11(18), pages 1-17, September.
    3. 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.
    4. Frostig, Esther & Zaks, Yaniv & Levikson, Benny, 2007. "Optimal pricing for a heterogeneous portfolio for a given risk factor and convex distance measure," Insurance: Mathematics and Economics, Elsevier, vol. 40(3), pages 459-467, May.
    5. Xu, Maochao & Hu, Taizhong, 2012. "Stochastic comparisons of capital allocations with applications," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 293-298.
    6. Jiří Valecký, 2016. "Modelling Claim Frequency in Vehicle Insurance," Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis, Mendel University Press, vol. 64(2), pages 683-689.
    7. Jiří Valecký, 2017. "Calculation of Solvency Capital Requirements for Non-life Underwriting Risk Using Generalized Linear Models," Prague Economic Papers, Prague University of Economics and Business, vol. 2017(4), pages 450-466.
    8. Zaks, Yaniv & Tsanakas, Andreas, 2014. "Optimal capital allocation in a hierarchical corporate structure," Insurance: Mathematics and Economics, Elsevier, vol. 56(C), pages 48-55.
    9. Xu, Maochao & Mao, Tiantian, 2013. "Optimal capital allocation based on the Tail Mean–Variance model," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 533-543.

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