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Approximating the Finite-Time Ruin Probability under Interest Force


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  • Brekelmans, R.C.M.
  • De Waegenaere, A.M.B.

    (Tilburg University, Center for Economic Research)


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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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2000-111.

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Date of creation: 2000
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Handle: RePEc:dgr:kubcen:2000111

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Keywords: interest rate; probability;

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  1. 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.
  2. 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.
  3. Sundt, Bjorn & Teugels, Jozef L., 1995. "Ruin estimates under interest force," Insurance: Mathematics and Economics, Elsevier, vol. 16(1), pages 7-22, April.
  4. Boogaert, P. & Haezendonck, J., 1989. "Delay in claim settlement," Insurance: Mathematics and Economics, Elsevier, vol. 8(4), pages 321-330, December.
  5. 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.
  6. Paulsen, Jostein, 1998. "Ruin theory with compounding assets -- a survey," Insurance: Mathematics and Economics, Elsevier, vol. 22(1), pages 3-16, May.
  7. 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.
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Cited by:
  1. Didier Rullière & Stéphane Loisel, 2005. "The win-first probability under interest force," Post-Print hal-00165791, HAL.
  2. Jostein Paulsen, 2008. "Ruin models with investment income," Papers 0806.4125,, revised Dec 2008.
  3. 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.
  4. 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.


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