Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-27T13:45:26.998Z Has data issue: false hasContentIssue false
  • English
  • Français

ASYMPTOTIC RUIN PROBABILITIES IN FINITE HORIZON WITH SUBEXPONENTIAL LOSSES AND ASSOCIATED DISCOUNT FACTORS

Published online by Cambridge University Press:  12 December 2005

Qihe Tang
Qihe Tang
Affiliation:
Department of Statistics and Actuarial Science, The University of Iowa, Iowa City, IA 52242-1409, Department of Mathematics and Statistics, Concordia University, Montreal, Quebec, H4B 1R6, Canada, E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Consider a discrete-time insurance risk model with risky investments. Under the assumption that the loss distribution belongs to a certain subclass of the subexponential class, Tang and Tsitsiashvili (Stochastic Processes and Their Applications 108(2): 299–325 (2003)) established a precise estimate for the finite time ruin probability. This article extends the result both to the whole subexponential class and to a nonstandard case with associated discount factors.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 20 , Issue 1 , January 2006 , pp. 103 - 113
Copyright
© 2006 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Cai, J. (2002). Discrete time risk models under rates of interest. Probability in the Engineering and Informational Sciences 16(3): 309–324.Google Scholar
Cai, J. (2002). Ruin probabilities with dependent rates of interest. Journal of Applied Probability 39(2): 312–323.Google Scholar
Cai, J. (2004). Ruin probabilities and penalty functions with stochastic rates of interest. Stochastic Processes and Their Applications 112(1): 53–78.Google Scholar
Cai, J. & Dickson, D.C.M. (2004). Ruin probabilities with a Markov chain interest model. Insurance: Mathematics and Economics 35(3): 513–525.Google Scholar
Cline, D.B.H. (1986). Convolution tails, product tails and domains of attraction. Probability Theory and Related Fields 72(4): 529–557.Google Scholar
Cline, D.B.H. & Samorodnitsky, G. (1994). Subexponentiality of the product of independent random variables. Stochastic Processes and Their Applications 49(1): 75–98.Google Scholar
Embrechts, P. & Goldie, C.M. (1980). On closure and factorization properties of subexponential and related distributions. Journal of the Australian Mathematical Society, Series A 29(2): 243–256.Google Scholar
Embrechts, P., Klüppelberg, C., & Mikosch, T. (1997). Modelling extremal events for insurance and finance. Berlin: Springer-Verlag.CrossRef
Esary, J.D., Proschan, F., & Walkup, D.W. (1967). Association of random variables, with applications. Annals of Mathematical Statistics 38(5): 1466–1474.Google Scholar
Gaier, J. & Grandits, P. (2002). Ruin probabilities in the presence of regularly varying tails and optimal investment. Insurance: Mathematics and Economics 30(2): 211–217.Google Scholar
Gaier, J., Grandits, P., & Schachermayer, W. (2003). Asymptotic ruin probabilities and optimal investment. Annals of Applied Probability 13(3): 1054–1076.Google Scholar
Hipp, C. & Plum, M. (2000). Optimal investment for insurers. Insurance: Mathematics and Economics 27(2): 215–228.Google Scholar
Liu, C.S. & Yang, H. (2004). Optimal investment for an insurer to minimize its probability of ruin. North American Actuary Journal 8(2): 11–31.Google Scholar
Nyrhinen, H. (1999). On the ruin probabilities in a general economic environment. Stochastic Processes and Their Applications 83(2): 319–330.Google Scholar
Nyrhinen, H. (2001). Finite and infinite time ruin probabilities in a stochastic economic environment. Stochastic Processes and Their Applications 92(2): 265–285.Google Scholar
Resnick, S.I. & Willekens, E. (1991). Moving averages with random coefficients and random coefficient autoregressive models. Communications in Statistics—Stochastic Models 7(4): 511–525.Google Scholar
Tang, Q. & Tsitsiashvili, G. (2003). Precise estimates for the ruin probability in finite horizon in a discrete-time model with heavy-tailed insurance and financial risks. Stochastic Processes and Their Applications 108(2): 299–325.Google Scholar
Tang, Q. & Tsitsiashvili, G. (2003). Randomly weighted sums of subexponential random variables with application to ruin theory. Extremes 6(3): 171–188.Google Scholar
Tang, Q. & Tsitsiashvili, G. (2004). Finite and infinite time ruin probabilities in the presence of stochastic return on investments. Advances in Applied Probability 36(4): 1278–1299.Google Scholar