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Modified Recursions for a Class of Compound Distributions

  • Karl-Heinz Waldmann (a1)
Abstract

Recursions are derived for a class of compound distributions having a claim frequency distribution of the well known (a,b)-type. The probability mass function on which the recursions are usually based is replaced by the distribution function in order to obtain increasing iterates. A monotone transformation is suggested to avoid an underflow in the initial stages of the iteration. The faster increase of the transformed iterates is diminished by use of a scaling function. Further, an adaptive weighting depending on the initial value and the increase of the iterates is derived. It enables us to manage an arbitrary large portfolio. Some numerical results are displayed demonstrating the efficiency of the different methods. The computation of the stop-loss premiums using these methods are indicated. Finally, related iteration schemes based on the cumulative distribution function are outlined.

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Copyright
References
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Gerber, H.U. (1979) An Introduction to Mathematical Risk Theory. Huebner Foundation Monograph 8, Philadelphia.
Kuon, S., Radke, A. and Reich, A. (1993) An Appropriate Way to Switch from the Individual Risk Model to the Collective One. ASTIN Bulletin 23, 2354.
Panjer, H.H. and Wang, S. (1993) On the stability of recursive formulas. ASTIN Bulletin 23, 227258.
Panjer, H.H. and Willmot, G.E. (1986) Computational aspects of recursive evaluation of compound distributions. Insurance: Mathematics and Economics 5, 113116.
Panjer, H.H. and Willmot, G.E. (1992) Insurance Risk Models. Society of Actuaries, Schaumburg, IL.
Sundt, B. (1991) An Introduction to Non-Life Insurance Mathematics (2. Auflage). Verlag Versicherungswirtschaft, Karlsruhe.
Waldmann, K.-H. (1994) On the exact calculation of the aggregate claims distribution in the individual life model. ASTIN Bulletin 24, 8996.
Waldmann, K.-H. (1995) Exact calculation of the aggregate claims distribution in the individual life model by use of an n-layer model. Blätter der DGVM, Band XXII, 279287.
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ASTIN Bulletin: The Journal of the IAA
  • ISSN: 0515-0361
  • EISSN: 1783-1350
  • URL: /core/journals/astin-bulletin-journal-of-the-iaa
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