The win-first probability under interest force
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.
|Date of creation:||16 Dec 2005|
|Date of revision:|
|Publication status:||Published, Insurance Mathematics and Economics, 2005, 37, 3, 421-442|
|Note:||View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00165791/en/|
|Contact details of provider:|| Web page: https://hal.archives-ouvertes.fr/|
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- 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.
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- 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.
- Brekelmans, Ruud & De Waegenaere, Anja, 2001.
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Insurance: Mathematics and Economics,
Elsevier, vol. 29(2), pages 217-229, October.
- Brekelmans, R.C.M. & De Waegenaere, A.M.B., 2000. "Approximating the Finite-Time Ruin Probability under Interest Force," Discussion Paper 2000-111, Tilburg University, Center for Economic Research.
- Sundt, Bjorn & Teugels, Jozef L., 1995. "Ruin estimates under interest force," Insurance: Mathematics and Economics, Elsevier, vol. 16(1), pages 7-22, April.
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