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Ruin probabilities with dependent rates of interest

Part of: Special processes Survival analysis and censored data

Published online by Cambridge University Press:  14 July 2016

Jun Cai
Jun Cai*
Affiliation:
University of Melbourne
*
∗ Current address: Department of Statistics and Actuarial Sciences, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1. Email address: jcai@icarus.math.uwaterloo.ca
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Abstract

In this paper, we study ruin probabilities in two generalized risk models. The effects of timing of payments and interest on the ruin probabilities in the models are considered. The rates of interest are assumed to have a dependent autoregressive structure. Generalized Lundberg inequalities for the ruin probabilities are derived by a renewal recursive technique. An illustrative application is given to the compound binomial risk process.

Keywords

Ruin probabilityrate of interestLundberg inequalityNWUCcompound binomial risk process

MSC classification

Primary: 60K10: Applications (reliability, demand theory, etc.) 60K25: Queueing theory
Secondary: 62N05: Reliability and life testing
Type
Research Papers
Information
Journal of Applied Probability , Volume 39 , Issue 2 , June 2002 , pp. 312 - 323
Copyright
Copyright © Applied Probability Trust 2002 

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References

Asmussen, S. (2000). Ruin Probabilities. World Scientific, Singapore.Google Scholar
Cai, J. (2002). Discrete time risk models under rates of interest. Prob. Eng. Inf. Sci. 16, 309–324.Google Scholar
Cao, J., and Wang, Y. (1991). The NBUC and NWUC classes of life distributions. J. Appl. Prob. 28, 473–479.Google Scholar
Cheng, S., Gerber, H. U., and Shiu, E. S. W. (2000). Discounted probabilities and ruin theory in the compound binomial model. Insurance Math. Econom. 26, 239–250.Google Scholar
DeVylder, F. E., and Marceau, E. (1996). Classical numerical ruin probabilities. Scand. Actuarial J. 1996, 109–123.Google Scholar
Grandell, J. (1991). Aspects of Risk Theory. Springer, New York.Google Scholar
Grandell, J. (1997). Mixed Poisson Processes. Chapman and Hall, London.CrossRefGoogle Scholar
Kellison, S. (1991). The Theory of Interest, 2nd edn. IRWIN, Boston.Google Scholar
Rolski, T., Schmidli, V., Schmidt, V., and Teugels, J. L. (1999). Stochastic Processes for Insurance and Finance. John Wiley, Chichester.Google Scholar
Ross, S. (1996). Stochastic Processes, 2nd edn. John Wiley, New York.Google Scholar
Sundt, B., and Teugels, J. L. (1995). Ruin estimates under interest force. Insurance Math. Econom. 16, 7–22.Google Scholar
Sundt, B., and Teugels, J. L. (1997). The adjustment function in ruin estimates under interest force. Insurance Math. Econom. 19, 85–94.Google Scholar
Willmot, G. E. (1996). A non-exponential generalization of an inequality arising in queueing and insurance risk. J. Appl. Prob. 33, 176–183.CrossRefGoogle Scholar
Willmot, G. E., and Lin, X. S. (2001). Lundberg Approximations for Compound Distributions with Insurance Applications. Springer, New York.Google Scholar
Yang, H. (1999). Non-exponential bounds for ruin probability with interest effect included. Scand. Actuarial J. 1999, 66–79.Google Scholar