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.
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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, R.C.M. & De Waegenaere, A.M.B., 2000.
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2000-111, Tilburg University, Center for Economic Research.
- 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.
- 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.
- Didier Rullière & Stéphane Loisel, 2004. "Another look at the Picard-Lefèvre formula for finite-time ruin probabilities," Post-Print hal-00379412, HAL.
- Sundt, Bjorn & Teugels, Jozef L., 1995. "Ruin estimates under interest force," Insurance: Mathematics and Economics, Elsevier, vol. 16(1), pages 7-22, April.
- 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.
- 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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