Estimates for the ruin probability in the classical risk model with constant interest force in the presence of heavy tails. (English) Zbl 1074.91029

The paper studies the ruin probability in the classical risk model with homogeneous Poisson arrival process, constant premium rate and constant interest force. The case where the claim size is heavy-tailed, i.e. the equilibrium distribution function of the claim size belongs to a subclass of subexponential distributions, is considered. Accurate two-sided estimates for the ruin probability are obtained by reduction from the classical model without interest force. Some examples and numerical results are presented.


91B30 Risk theory, insurance (MSC2010)
Full Text: DOI


[1] Asmussen, S., Subexponential asymptotics for stochastic processes: extremal behaviour, stationary distributions and first passage probabilities, The annals of applied probability, 8, 354-374, (1998) · Zbl 0942.60034
[2] Asmussen, S., 2000. Ruin Probabilities. World Scientific, Singapore. · Zbl 0960.60003
[3] Asmussen, S.; Kalashnikov, V.; Klüppelberg, C.; Konstantinides, D.; Tsitsiashvili, G.Sh., A local limit theorem for random walk maxima with heavy-tails, Statistics and probability letters, 56, 399-404, (2002) · Zbl 0997.60047
[4] Bingham, N.H., Goldie, C.M., Teugels, J.L., 1987. Regular Variation. Cambridge University Press, Cambridge. · Zbl 0617.26001
[5] Embrechts, P.; Veraverbeke, N., Estimates for the probability of ruin with special emphasis on the possibility of large claims, Insurance: mathematics and economics, 1, 55-72, (1982) · Zbl 0518.62083
[6] Embrechts, P., Klüppelberg, C., Mikosch, T., 1997. Modelling Extremal Events for Insurance and Finance. Springer, New York. · Zbl 0873.62116
[7] Feller, W., 1971. An Introduction to Probability Theory and its Applications, vol. II. Wiley, New York. · Zbl 0219.60003
[8] Kalashnikov, V.V.; Konstantinides, D., Ruin under interest force and subexponential claims: a simple treatment, Insurance: mathematics and economics, 27, 145-149, (2000) · Zbl 1056.60501
[9] Kalashnikov, V.V.; Tsitsiashvili, G.Sh., Tails of waiting times and their bounds, Queueing systems, 32, 257-283, (1999) · Zbl 0997.60106
[10] Kalashnikov, V.V., Tsitsiashvili, G.Sh., 2000. Tight approximation of basic characteristics of classical and non-classical surplus process. ARCH00V210(2000-9), vol. 2, pp. 251-293.
[11] Klüppelberg, C., Stadtmüller, U., 1998. Ruin probabilities in the presence of heavy-tails and interest rates. Scandinavian Actuarial Journal, 49-58.
[12] Mikosch, T.; Nagaev, A., Rates in approximations to ruin probabilities for heavy-tailed distributions, Extremes, 4, 1, 67-78, (2001) · Zbl 1003.60050
[13] Rolski, T., Schmidli, H., Schmidt, V., Teugels, J., 1999. Stochastic Processes for Insurance and Finance. Wiley, New York. · Zbl 0940.60005
[14] Sundt, B.; Teugels, J.L., Ruin estimates under interest force, Insurance: mathematics and economics, 16, 7-22, (1995) · Zbl 0838.62098
[15] Sundt, B.; Teugels, J.L., The adjustment function in ruin estimates under interest force, Insurance: mathematics and economics, 19, 85-94, (1997) · Zbl 0910.62107
[16] Tang, Q.H.; Su, C.; Jiang, T.; Zhang, J.S., Large deviations for heavy-tailed random sums in compound renewal model, Statistics and probability letters, 52, 91-100, (2001) · Zbl 0977.60034
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.