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Exponential bounds for ruin probability in two moving average risk models with constant interest rate. (English) Zbl 1143.62071
The authors consider two discrete-time moving average risk models with a constant interest rate. The first model generalizes the one by H. U. Gerber [Insur. Math. Econ. 1, 177–184 (1982; Zbl 0505.62086)], and the moving average is used to model the annual gains. The second model extends the risk model by H. Yang [Scand. Actuarial J. 1999, No. 1, 66–79 (1999; Zbl 0922.62113)] to the case where both the premiums process and the claims process are correlated. For the two considered models, the authors derive exponential bounds for the ruin probability of an infinite time horizon using a martingale approach.

62P05 Applications of statistics to actuarial sciences and financial mathematics
91B30 Risk theory, insurance (MSC2010)
60G42 Martingales with discrete parameter
Full Text: DOI
[1] Gerber, H. U.: Ruin theory in the linear model. Insurance: Mathematics and Economics, 1, 177–184 (1982) · Zbl 0505.62086 · doi:10.1016/0167-6687(82)90008-7
[2] Bowers, N. L., Gerber, H. U., Hickman, J. C., Jones, D. A., Nesbitt, C. J.: Actuarial Mathematics, 2nd edition, The Society of Actuaries, Schaumburg, 1997 · Zbl 0634.62107
[3] Yang, H. L., Zhang, L. H.: Martingale method for ruin probability in an autoregressive model with constant interest rate. Probability in the Engineering and Informational Sciences, 17, 183–198 (2003) · Zbl 1065.62182 · doi:10.1017/S0269964803172026
[4] Sundt, B., Teugels, J. L.: Ruin estimates under interest force. Insurance: Mathematics and Economics, 16, 7–22 (1995) · Zbl 0838.62098 · doi:10.1016/0167-6687(94)00023-8
[5] Sundt, B., Teugels, J. L.: The adjustment function in ruin estimates under interest force. Insurance: Mathematics and Economics, 19, 85–94 (1997) · Zbl 0910.62107 · doi:10.1016/S0167-6687(96)00012-1
[6] Yang, H. L.: Non-exponential Bounds for Ruin Probability with Interest Effect Included. Scandinavian Actuarial Journal, 66–79 (1998) · Zbl 0922.62113
[7] Konstantinides, D., Tang, Q. H., Tsitsiashvili, G.: Estimates for the ruin probability in the classical risk model with constant interest force in the presence of heavy tails. Insurance: Mathematics and Economics, 31, 447–460 (2002) · Zbl 1074.91029 · doi:10.1016/S0167-6687(02)00189-0
[8] Cai, J.: Discrete time risk models under rates of interest. Probability in the Engineering and Informational Sciences, 16, 309–324 (2002) · Zbl 1031.91057 · doi:10.1017/S0269964802163030
[9] Cai, J.: Ruin probabilities with dependent rates of interest. Journal of Applied Probability, 39, 312–323 (2002) · Zbl 1007.60096 · doi:10.1239/jap/1025131428
[10] Rolski, T., Schmidli, H., Schmidt, V., Teugels, J.: Stochastic Processes for Insurance and Finance, John Wiley & Sons Ltd, New York, 1999 · Zbl 0940.60005
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