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Pure risk premiums under deductibles. A quantitative management in actuarial practice


  • Krzysztof Burnecki
  • Joanna Nowicka-Zagrajek
  • Aleksander Weron


It is common practice in most insurance lines for the coverage to be restricted by a deductible. In the paper we investigate the influence of deductibles on pure risk premiums. We derive simple but practical formulae for premiums under franchise, fix amount, proportional, limited proportional and disappearing deductibles in terms of the limited expected value function. Next, we apply the results to typical loss distributions, i.e. lognormal, Pareto, Burr, Weibull and gamma. Finally, we analyse a loss data of one of the power companies. We fit distributions to the data and show how the choice of the distribution and a deductible influences the premium.

Suggested Citation

  • Krzysztof Burnecki & Joanna Nowicka-Zagrajek & Aleksander Weron, 2004. "Pure risk premiums under deductibles. A quantitative management in actuarial practice," HSC Research Reports HSC/04/05, Hugo Steinhaus Center, Wroclaw University of Technology.
  • Handle: RePEc:wuu:wpaper:hsc0405

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    File Function: Draft, 2004
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    References listed on IDEAS

    1. Broszkiewicz-Suwaj, E & Makagon, A & Weron, R & Wyłomańska, A, 2004. "On detecting and modeling periodic correlation in financial data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 336(1), pages 196-205.
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    Cited by:

    1. Julie Thøgersen, 2016. "Optimal Premium as a Function of the Deductible: Customer Analysis and Portfolio Characteristics," Risks, MDPI, Open Access Journal, vol. 4(4), pages 1-19, November.

    More about this item


    Insurance risk premium; Deductible; Limited expected value function;

    JEL classification:

    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies


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