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Approximating the finite-time ruin probability under interest force

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  • Brekelmans, Ruud
  • De Waegenaere, Anja

Abstract

We present an algorithm to determine both a lower and an upper bound for the finite-time probability of ruin for a risk process with constant interest force. We split the time horizon into smaller intervals of equal length and consider the probability of ruin in case premium income for a time interval is received at the beginning (resp. end) of that interval, which yields a lower (resp. upper) bound.For both bounds we present a renewal equation which depends on the distribution of the present value of the aggregate claim amount in a time interval.This distribution is determined through a generalization of Panjer's (1981) recursive method.
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Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:29:y:2001:i:2:p:217-229
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    References listed on IDEAS

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    1. Paulsen, Jostein, 1998. "Ruin theory with compounding assets -- a survey," Insurance: Mathematics and Economics, Elsevier, vol. 22(1), pages 3-16, May.
    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. Boogaert, P. & Haezendonck, J., 1989. "Delay in claim settlement," Insurance: Mathematics and Economics, Elsevier, vol. 8(4), pages 321-330, December.
    4. Dickson, David C. M. & Waters, Howard R., 1999. "Ruin probabilities with compounding assets," Insurance: Mathematics and Economics, Elsevier, vol. 25(1), pages 49-62, September.
    5. Boogaert, P. & De Waegenaere, A., 1990. "Macro-economic version of a classical formula in risk theory," Insurance: Mathematics and Economics, Elsevier, vol. 9(2-3), pages 155-162, September.
    6. De Vylder, F. & Goovaerts, M. J., 1988. "Recursive calculation of finite-time ruin probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 7(1), pages 1-7, January.
    7. Gjessing, Håkon K. & Paulsen, Jostein, 1997. "Present value distributions with applications to ruin theory and stochastic equations," Stochastic Processes and their Applications, Elsevier, vol. 71(1), pages 123-144, October.
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    Cited by:

    1. Cardoso, Rui M. R. & R. Waters, Howard, 2003. "Recursive calculation of finite time ruin probabilities under interest force," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 659-676, December.
    2. Paulsen, Jostein & Kasozi, Juma & Steigen, Andreas, 2005. "A numerical method to find the probability of ultimate ruin in the classical risk model with stochastic return on investments," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 399-420, June.
    3. Jostein Paulsen, 2008. "Ruin models with investment income," Papers 0806.4125, arXiv.org, revised Dec 2008.
    4. Rulliere, Didier & Loisel, Stephane, 2005. "The win-first probability under interest force," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 421-442, December.

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    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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