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Maximizing Compound Poisson Stop-Loss Premiums Numerically with Given Mean and Variance

Author

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  • Kaas, R.
  • Vanneste, M.
  • Goovaerts, M.J.

Abstract

This paper describes a technique to find the maximal stop-loss premiums in a given retention for a compound Poisson risk with known parameter, and known mean and variance of the claims. Restricting to an arithmetic and finite support of the claims, one gets an optimization problem of a non-linear function with a computable gradient, under linear constraints. Numeraical results are given contrasting the method with the method of a previous paper, where only diatomic distributions were considered.

Suggested Citation

  • Kaas, R. & Vanneste, M. & Goovaerts, M.J., 1992. "Maximizing Compound Poisson Stop-Loss Premiums Numerically with Given Mean and Variance," ASTIN Bulletin, Cambridge University Press, vol. 22(2), pages 225-233, November.
    • Handle: RePEc:cup:astinb:v:22:y:1992:i:02:p:225-233_00
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    Cited by:

    1. De Vylder, F. & Marceau, E., 1996. "The numerical solution of the Schmitter problems: Theory," Insurance: Mathematics and Economics, Elsevier, vol. 19(1), pages 1-18, December.
    2. Hansjörg Albrecher & José Carlos Araujo-Acuna, 2022. "On The Randomized Schmitter Problem," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 515-535, June.
    3. De Vylder, F. & Goovaerts, M. & Marceau, E., 1997. "The solution of Schmitter's simple problem: Numerical illustration," Insurance: Mathematics and Economics, Elsevier, vol. 20(1), pages 43-58, June.
    4. De Vylder, F. & Goovaerts, M. & Marceau, E., 1997. "The bi-atomic uniform minimal solution of Schmitter's problem," Insurance: Mathematics and Economics, Elsevier, vol. 20(1), pages 59-78, June.

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