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The win-first probability under interest force

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  • Didier Rullière

    ()
    (SAF - Laboratoire de Sciences Actuarielle et Financière - Université Claude Bernard - Lyon I : EA2429)

  • Stéphane Loisel

    ()
    (SAF - Laboratoire de Sciences Actuarielle et Financière - Université Claude Bernard - Lyon I : EA2429)

Abstract

In a classical risk model under constant interest force, we study the probability that the surplus of an insurance company reaches an upper barrier before a lower barrier. We define this probability as win-first probability. Borrowing ideas from life-insurance theory, hazard rates of the maximum of the surplus before ruin, regarded as a remaining future lifetime random variable, are studied, and provide an original derivation of the win-first probability. We propose an algorithm to efficiently compute this risk-return indicator and its derivatives in the general case, as well as bounds of these quantities. The efficiency of the proposed algorithm is compared with adaptations of other existing methods, and its interest is illustrated by the computation of the expected amount of dividends paid until ruin in a risk model with a dividend barrier strategy.

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Bibliographic Info

Paper provided by HAL in its series Post-Print with number hal-00165791.

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Date of creation: 16 Dec 2005
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Publication status: Published, Insurance Mathematics and Economics, 2005, 37, 3, 421-442
Handle: RePEc:hal:journl:hal-00165791

Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00165791/en/
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Keywords: Ruin probability; hazard rate; upper absorbing barrier; constant interest force; risk-return indicator; win-first probability;

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  1. Wang, Nan & Politis, Konstadinos, 2002. "Some characteristics of a surplus process in the presence of an upper barrier," Insurance: Mathematics and Economics, Elsevier, vol. 30(2), pages 231-241, April.
  2. Sundt, Bjorn & Teugels, Jozef L., 1995. "Ruin estimates under interest force," Insurance: Mathematics and Economics, Elsevier, vol. 16(1), pages 7-22, April.
  3. Brekelmans, Ruud & De Waegenaere, Anja, 2001. "Approximating the finite-time ruin probability under interest force," Insurance: Mathematics and Economics, Elsevier, vol. 29(2), pages 217-229, October.
  4. Konstantinides, Dimitrios & Tang, Qihe & Tsitsiashvili, Gurami, 2002. "Estimates for the ruin probability in the classical risk model with constant interest force in the presence of heavy tails," Insurance: Mathematics and Economics, Elsevier, vol. 31(3), pages 447-460, December.
  5. Rulliere, Didier & Loisel, Stephane, 2004. "Another look at the Picard-Lefevre formula for finite-time ruin probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 187-203, October.
  6. Sundt, Bjorn & Teugels, Jozef L., 1997. "The adjustment function in ruin estimates under interest force," Insurance: Mathematics and Economics, Elsevier, vol. 19(2), pages 85-94, April.
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Cited by:
  1. Yuan, Haili & Hu, Yijun, 2008. "Absolute ruin in the compound Poisson risk model with constant dividend barrier," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2086-2094, October.

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