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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: qtang@mathstat.concordia.ca
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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

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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