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Some Mathematical Aspects of Price Optimisation

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Listed:
  • Y. Bai
  • E. Hashorva
  • G. Ratovomirija
  • M. Tamraz

Abstract

Calculation of an optimal tariff is a principal challenge for pricing actuaries. In this contribution we are concerned with the renewal insurance business discussing various mathematical aspects of calculation of an optimal renewal tariff. Our motivation comes from two important actuarial tasks, namely a) construction of an optimal renewal tariff subject to business and technical constraints, and b) determination of an optimal allocation of certain premium loadings. We consider both continuous and discrete optimisation and then present several algorithmic sub-optimal solutions. Additionally, we explore some simulation techniques. Several illustrative examples show both the complexity and the importance of the optimisation approach.

Suggested Citation

  • Y. Bai & E. Hashorva & G. Ratovomirija & M. Tamraz, 2016. "Some Mathematical Aspects of Price Optimisation," Papers 1605.05814, arXiv.org.
    • Handle: RePEc:arx:papers:1605.05814
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    References listed on IDEAS

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    1. Asimit, Alexandru V. & Chi, Yichun & Hu, Junlei, 2015. "Optimal non-life reinsurance under Solvency II Regime," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 227-237.
    2. Michael Bartholomew-Biggs, 2008. "Nonlinear Optimization with Engineering Applications," Springer Optimization and Its Applications, Springer, number 978-0-387-78723-7, June.
    3. Asimit, Alexandru V. & Badescu, Alexandru M. & Haberman, Steven & Kim, Eun-Seok, 2016. "Efficient risk allocation within a non-life insurance group under Solvency II Regime," Insurance: Mathematics and Economics, Elsevier, vol. 66(C), pages 69-76.
    4. Asimit, Alexandru V. & Badescu, Alexandru M. & Cheung, Ka Chun, 2013. "Optimal reinsurance in the presence of counterparty default risk," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 690-697.
    5. David G. Luenberger & Yinyu Ye, 2016. "Linear and Nonlinear Programming," International Series in Operations Research and Management Science, Springer, edition 4, number 978-3-319-18842-3, April.
    6. Ma, Cheng & Zhang, Liansheng, 2015. "On an exact penalty function method for nonlinear mixed discrete programming problems and its applications in search engine advertising problems," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 642-656.
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