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

Gaofeng Zong

Front. Math. China ›› 2010, Vol. 5 ›› Issue (4) : 801 -809.

PDF (145KB)
Front. Math. China ›› 2010, Vol. 5 ›› Issue (4) : 801 -809. DOI: 10.1007/s11464-010-0071-z
Research Article
RESEARCH ARTICLE

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

Author information +
History +
PDF (145KB)

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

Cite this article

Download citation ▾
Gaofeng Zong. Finite-time ruin probability of a nonstandard compound renewal risk model with constant force of interest. Front. Math. China, 2010, 5(4): 801-809 DOI:10.1007/s11464-010-0071-z

登录浏览全文

4963

注册一个新账户 忘记密码

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, 2000, Singapore: World Scientific

[3]

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

[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, 1997, Berlin: Springer.

[11]

Goldie C. M., Klüppelberg C. Alder R. J., Feldman R. E., Taqqu M. S. Subexponential distributions. A Practical Guide to Heavy-Tails: Statistical Techniques and Applications, 1998, Basel: Birkhäuser, 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. Some concepts of dependence. Ann Math Statist, 1966, 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, 2001, New York: Wiley.

[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.

AI Summary AI Mindmap
PDF (145KB)

706

Accesses

0

Citation

Detail

Sections
Recommended

AI思维导图

/