# THE INDUCTIVE METHOD FOR INFINITE-TIME RUIN PROBABLILITY IN QUOTA- (α, β) REINSURANCE MODEL

### Abstract

In this article, we investigate a risk model with a quota-(α, β) reinsurance contract. The premium process and claim process are assumed to be independent sequences of indentically distributed random variables. Using inductive method, we obtain upper bound of infinite-time ruin probability of an insurance company.

### References

D.C.M. Dickson. Insurance Risk and Ruin. Cambridge University Presss, 2006.

H. Yang. Non-exponential Bounds for Ruin Probability with Interest Effect Included. Scandinavian Actuarial Journal, 1: 66-79, 1999.

J. Cai. Ruin Probabilities with Dependent Rates of Interest. Journal of Applied Probability, 39(2):312-323, 2002.

J. Cai, D.C.M. Dickson. Ruin probabilities with a Markov chain interest model. Insurance: Mathematics and Economics, 35: 513-525, 2004.

Q. Tang. The Ruin Probability of a Discrete Time Risk Model under Constant Interest Rate with Heavy Tails. Scandinavian Actuarial Journal. 2004, 3: 229-240.

X. Wei, Y. Hu. Ruin probabilities for discrete time risk models with stochastic rates of interest. Statistics & Probability Letters, 78: 707-715, 2008.

C. Weng, Y. Zhang, K.S. Tan. Ruin probabilities in a discrete time risk model with dependent risks of heavy tail. Scandinavian Actuarial Journal, 3: 205-218, 2009.

X. Lin, Z. Dongjin, Z. Yanru. Minimizing Upper Bound of Ruin Probability Under Discrete Risk Model with Markov Chain Interest Rate. Communications in Statistics - Theory and Methods, 44(4): 810-822, 2015.

P.D. Quang. Ruin Probability in a Generalised Risk Process under Rates of Interest with Homogenous Markov Chain. East Asian Journal on Applied Mathematics, 4(3):283-300, 2014.

B.K. Dam, N.Q. Chung. The Martingale Method for Probability of Ultimate Ruin Under Quota Reinsurance Model. Journal of Statistics & Application Probability, 5(3):411-419, 2016.

B.K. Dam, N.Q. Chung. On Finite- Time Ruin Probabilities in a Risk Model under Quota Share Reinsurance Contract. Applied Mathematical Sciences, 11(35):2609-2629, 2017.

J.Cai and D.C.M. Dickson. Upper bounds for ultimate ruin probabilities in the Sparre Andersen model with interest. Insurance: Mathematics and Economics, 32: 61-71, 2003

*UTEHY Journal of Science and Technology*,

*25*, 71-73. Retrieved from http://tapchi.utehy.edu.vn/index.php/jst/article/view/359