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On Joint Ruin Probabilities of a Two-Dimensional Risk Model with Constant Interest Rate

  • Zechun Hu (a1) and Bin Jiang (a2)

Abstract

In this note we consider the two-dimensional risk model introduced in Avram, Palmowski and Pistorius (2008) with constant interest rate. We derive the integral-differential equations of the Laplace transforms, and asymptotic expressions for the finite-time ruin probabilities with respect to the joint ruin times T max(u 1,u 2) and T min(u 1,u 2) respectively.

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Copyright

Corresponding author

Postal address: Department of Mathematics, Nanjing University, Nanjing 210093, China. Email address: huzc@nju.edu.cn
∗∗ Postal address: Department of Econometrics and Business Statistics, Monash University, Clayton, Victoria 3800, Australia. Email address: bin.jiang@monash.edu

References

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[1] Asmussen, S. (2000). Ruin Probabilities. World Scientific, River Edge, NJ.
[2] Avram, F., Palmowski, Z. and Pistorius, M. (2008). A two-dismensional ruin problem on the positive quadrant. Insurance Math. Econom. 42, 227234.
[3] Cai, J. and Li, H. (2005). Multivariate risk model of phase type. Insurance Math. Econom. 36, 137152.
[4] Cai, J. and Li, H. (2007). Dependence properties and bounds for ruin probabilities in multivariate compound risk models. J. Multivariate Anal. 98, 757773.
[5] Chan, W.-S., Yang, H. and Zhang, L. (2003). Some results on ruin probabilities in a two-dimensional risk model. Insurance Math. Econom. 32, 345358.
[6] Gerber, H. U. (1981). On the probability of ruin in the presence of a linear dividend barrier. Scand. Actuarial J. 1981, 105115.
[7] Li, J., Liu, Z. and Tang, Q. (2007). On the ruin probabilities of a bidimensional perturbed risk model. Insurance Math. Econom. 41, 185195.
[8] Paulsen, J. (2008). Ruin models with investment income. Prob. Surveys 5, 416434.
[9] Protter, P. E. (1992). Stochastic Integration and Differential Equations: A New Approach. Springer, Berlin.
[10] Rolski, T., Schmidli, H., Schimidt, V. and Teugels, J. (1999). Stochastic Processes for Finance and Insurance. John Wiley, Chichester.
[11] Yuen, K. C., Guo, J. and Wu, X. (2006). On the first time of ruin in the bivariate compound Poisson model. Insurance Math. Econom. 38, 298308.

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On Joint Ruin Probabilities of a Two-Dimensional Risk Model with Constant Interest Rate

  • Zechun Hu (a1) and Bin Jiang (a2)

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