Abstract
For the renewal risk model with subexponential claim sizes, we established for the finite time ruin probability a lower asymptotic estimate as initial surplus increases, subject to the demand that it should hold uniformly over all time horizons in an infinite interval. In the case of Poisson model, we also obtained the upper asymptotic formula so that an equivalent formula was derived. These extended a recent work partly on the topic from the case of Pareto-type claim sizes to the case of subexponential claim sizes and, simplified the proof of lower bound in Leipus and Siaulys ([9]).
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References
Asmussen, S.: Approximations for the probability of ruin within finite time. Scand. Actuar. J. (1), 31–57 (1984)
Asmussen, S.: Ruin probabilities. World Scientific Publishing Co., Inc., River Edge (2000)
Embrechts, P., Klüppelberg, C., Mikosch, T.: Modelling extremal events for insurance and finance. Springer, Berlin (1997)
Embrechts, P., Veraverbeke, N.: Estimates for the probability of ruin with special emphasis on the possibility of large claims. Insurance Math. Econom. 1(1), 55–72 (1982)
Goldie, C.M., Klüppelberg, C.: Subexponential distributions. In: Adler, R., Feldman, R., Taqqu, M.S. (eds.) A practical Guide to Heavy-Tails: Statistical Techniques and Applications. Birkhäuser, Boston (1998)
Kaas, R., Tang, Q.: Note on the tail behavior of random walk maxima with heavy tails and negative drift. N. Am. Actuar. J. 7(3), 57–61 (2003)
Klüppelberg, C., Mikosch, T.: Large deviations of heavy-tailed random sums with applications in insurance and finance. J. Appl. Probab. 34(2), 293–308 (1997)
Korshunov, D.A.: Large deviation probabilities for the maxima of sums of independent summands with a negative mean and a subexponential distribution. Theory Probab. Appl. 46(2), 355–365 (2003)
Leipus, R., Siaulys, J.: Asymptotic behaviour of the finite-time ruin probability under subexponential claim sizes. Insurance Math. Econom. 7(7), 1016–1027 (2006)
Ross, S.M.: Stochastic processes. John Wiley & Sons, Inc., New York (1983)
Tang, Q.: Uniform estimates for the tail probability of maxima over finite horizons with subexponential tails. Probab. Engrg. Inform. Sci. 18(1), 71–86 (2004a)
Tang, Q.: Asymptotics for the finite time ruin probability in the renewal model with consistent variation. Stoch. Models. 20(3), 281–297 (2004b)
Veraverbeke, N.: Asymptotic behaviour of Wiener-Hopf factors of a random walk. Stochastic Processes Appl. 5(1), 27–37 (1977)
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© 2009 ICST Institute for Computer Science, Social Informatics and Telecommunications Engineering
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Jiang, T. (2009). Asymptotic Behavior of Ruin Probability in Insurance Risk Model with Large Claims. In: Zhou, J. (eds) Complex Sciences. Complex 2009. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02466-5_103
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DOI: https://doi.org/10.1007/978-3-642-02466-5_103
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