Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-28T21:44:34.134Z Has data issue: false hasContentIssue false
  • English
  • Français

UPPER BOUNDS FOR RUIN PROBABILITY UNDER TIME SERIES MODELS

Published online by Cambridge University Press:  01 June 2006

Gary K. C. Chan  and
Hailiang Yang
Gary K. C. Chan
Affiliation:
Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong, E-mails: [email protected]; [email protected]
Hailiang Yang
Affiliation:
Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong, E-mails: [email protected]; [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

In this article, we consider an insurance risk model where the claim and premium processes follow some time series models. We first consider the model proposed in Gerber [2,3]; then a model with dependent structure between premium and claim processes modeled by using Granger's causal model is considered. By using some martingale arguments, Lundberg-type upper bounds for the ruin probabilities under both models are obtained. Some special cases are discussed.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 20 , Issue 3 , July 2006 , pp. 529 - 542
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

Boogaert, P., Haezendonck, J., & Delbaen, F. (1988). Limit theorems for the present value of the surplus of an insurance portfolio. Insurance: Mathematics and Economics 7: 131–138.Google Scholar
Gerber, H.U. (1981). On the probability of ruin in an autoregressive model. Bulletin of the Association of Swiss Actuaries 77: 131–141.Google Scholar
Gerber, H.U. (1982). Ruin theory in the linear model. Insurance: Mathematics and Economics 1: 177–184.Google Scholar
Granger, C.W.J. (1969). Investigating causal relations by econometric models and cross-spectral methods. Econometrica 37: 424–438.Google Scholar
Yang, H. (1999). Non-exponential bounds for ruin probability with interest effect included. Scandinavian Actuarial Journal 1999: 66–79.Google Scholar
Yang, H. & Zhang, L. (2003). Martingale method for ruin probability in an autoregressive model with constant interest rate. Probability in the Engineering and Informational Sciences 17: 183–198.Google Scholar