Finite-time ruin probability of a nonstandard compound renewal risk model with constant force of interest

Abstract

In this paper, we establish an exact asymptotic formula for the finite-time ruin probability of a nonstandard compound renewal risk model with constant force of interest in which claims arrive in groups, their sizes in one group are identically distributed but negatively dependent, and the inter-arrival times between groups are negatively dependent too.

Keywords

Finite-time ruin probability / compound renewal risk model / heavy tail / negative dependence

References

[1] Aleskeviciene A, Leipus R, Siaulys J. Tail behavior of random sums under consistent variation with applications to the compound renewal risk model. Extremes, 2008, 11(3): 261-279

[2] Asmussen S. Ruin Probabilities. Singapore: World Scientific, 2000

[3] Bingham N H, Goldie C M, Teugels J L. Regular Variation. Cambridge: Cambridge University Press, 1987

[4] Block H W, Savits T H, Shaked M. Some concepts of negative dependence. Ann Probab, 1982, 10: 765-772

[5] Chen Y, Zhang W P. Large deviations for random sums of negatively dependent random variables with consistently varying tails. Statistics Probability Letters, 2007, 77: 530-538

[6] Chen Y Q, Ng K W. The ruin probability of the renewal model with constant interest force and negatively dependent heavy-tailed claims. Insurance: Math and Economics, 2007, 40: 415-423

[7] Chen Y Q, Yuen K C. Sums of pairwise quasi-asymptotically independent random variables with consistent variation. Stochastic Models, 2009, 25: 76-89

[8] Cline D B H, Samorodnitsky G. Subexponentiality of the product of independent random variables. Stochastic Process Appl, 1994, 49: 75-98

[9] Ebrahimi N, Ghosh M. Multivariate negative dependence. Comm Statist A Theory Methods, 1981, 10: 307-337

[10] Embrechts P, Klüppelberg C, Mikosch T. Modelling Extremal Events for Insurance and Finance. Berlin: Springer, 1997

[11] Goldie C M, Klüppelberg C. Subexponential distributions. In: Alder R J, Feldman R E, Taqqu M S, eds. A Practical Guide to Heavy-Tails: Statistical Techniques and Applications. Basel: Birkhäuser, 1998, 435-459

[12] Kong F, Zong G. The finite-time ruin probability for ND claims with constant interest force. Statistics Probability Letters, 2008, 78: 3103-3109

[13] Lehmann E L. 1966. Some concepts of dependence. Ann Math Statist, 1996, 37: 1137-1153

[14] Matula P. A note on the almost sure convergence of sums of negatively dependent random variables. Stat Probab Lett, 1992, 15: 209-213

[15] Meerschaert M M, Scheffler H P. Limit Distributions for Sums of Independent Random Vectors. Heavy Tails in Theory and Practice. New York: Wiley, 2001

[16] Pemantle R. Towards a theory of negative dependence. J Math Phys, 2000, 41: 1371-1390

[17] Robert C Y, Segers J. Tails of random sums of a heavy-tailed number of light-tailed terms. Insurance: Mathematics and Economics, 2008, 43: 85-92

[18] Tang Q. The finite ruin probability of the compound Poisson model with constant interest force. J Appl Prob, 2005, 42: 608-619

[19] Tang Q. Insensitivity to negative dependence of the asymptotic behavior of precise large deviations. Electronic Journal of Probability, 2006, 11(4): 107-120

[20] Tang Q. Heavy tails of discounted aggregate claims in the continuous-time renewal model. J Appl Probab, 2007, 44(2): 285-294

[21] Tang Q, Su C, Jiang T, Zhang J. Large deviations for heavy-tailed random sums in compound renewal model. Stat Probab Lett, 2001, 52: 91-100

[22] Tang Q, Tsitsiashvili G. Precise estimates for the ruin probability in finite horizon in a discrete-time model with heavy-tailed insurance and financial risks. Stoch Process Appl, 2003, 108: 299-325

[23] Yang Y, Wang Y, Leipus R, Siaulys J. Asymptotics for tail probability of total claim amount with negatively dependent claim sizes andand its applications. Lithuanian Mathematical Journal, 2009, 49: 337-352

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