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FINITE HORIZON RUIN PROBABILITIES FOR RANDOM WALKS WITH HEAVY TAILED INCREMENTS

Published online by Cambridge University Press:  28 March 2013

Yingdong Lu
Yingdong Lu*
Affiliation:
IBM T.J. Watson Research Center, Yorktown Heights, NY 10598 E-mail: [email protected]
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Abstract

We study the asymptotic behavior of finite horizon ruin probabilities for random walks with heavy tailed increment via corrected diffusion approximation. We follow the main idea in [4] of inverting Fourier transformation, and the Fourier transformation is calculated through optimal stopping and a central limit theorem for renewal process.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 27 , Issue 2 , April 2013 , pp. 237 - 246
Copyright
Copyright © Cambridge University Press 2013

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References

1.Asmussen, S.Ruin probability. Singapore: World Scientific, 2000.CrossRefGoogle Scholar
2.Asmussen, S.Applied probability and queues, 2nd ed.New York: Springer-Verlag, 2003.Google Scholar
3.Asmussen, S. & Højgaard, B. (1999). Approximation for finite horizon ruin probabilities in the renewal model, Scandinavian Actuarial Journal 1999, 106–119CrossRefGoogle Scholar
4.Hogan, M. (1986). Comment on corrected diffusion approximations in certain random walk problems. Journal of Applied Probability 23 89–96.CrossRefGoogle Scholar
5.Lu, Y. (2009). Asymptotic estimation of finite horizon ruin probability for random walks with heavy tailed increments through corrected diffusion approximations. International Journal of Applied. Mathematics and Statistics. 14, 79–85.Google Scholar
6.Siegmund, D. (1979). Corrected diffusion approximation in certain random walk problems. Advances in Applied Probability 11, 701–719.CrossRefGoogle Scholar