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A PARTICULAR BIDIMENSIONAL TIME-DEPENDENT RENEWAL RISK MODEL WITH CONSTANT INTEREST RATES

Published online by Cambridge University Press:  07 March 2019

Ke-Ang Fu ,
Chang Ni  and
Hao Chen
Ke-Ang Fu
Affiliation:
School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou310018, China E-mail: [email protected]
Chang Ni
Affiliation:
School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou310018, China E-mail: [email protected]
Hao Chen
Affiliation:
School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou310018, China E-mail: [email protected]
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Abstract

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Consider a particular bidimensional risk model, in which two insurance companies divide between them in different proportions both the premium income and the aggregate claims. In practice, it can be interpreted as an insurer–reinsurer scenario, where the reinsurer takes over a proportion of the insurer's losses. Under the assumption that the claim sizes and inter-arrival times form a sequence of independent and identically distributed random pairs, with each pair obeying a dependence structure, an asymptotic expression for the ruin probability of this bidimensional risk model with constant interest rates is established.

Keywords

bidimensional risk modelconsistent variationproportional reinsuranceruin probabilitytime-dependence
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 34 , Issue 2 , April 2020 , pp. 172 - 182
Copyright
Copyright © Cambridge University Press 2019

References

1Asimit, A.V. & Badescu, A.L. (2010). Extremes on the discounted aggregate claims in a time dependent risk model. Scandinavian Actuarial Journal 2010(2): 93–104.CrossRefGoogle Scholar
2Avram, F., Palmowski, Z., & Pistorius, M. (2008). A two-dimensional ruin problem on the positive quadrant. Insurance Mathematics & Economics 42(1): 227–234.CrossRefGoogle Scholar
3Badescu, A.L., Cheung, E.C.K., & Rabehasaina, L. (2011). A two-dimensional risk model with proportional reinsurance. Journal of Applied Probability 48(3): 749–765.CrossRefGoogle Scholar
4Bingham, N.H., Goldie, C.M., & Teugels, J.L. (1987). Regular Variation. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
5Chan, W., Yang, H., & Zhang, L. (2003). Some results on ruin probabilities in a two-dimensional risk model. Insurance Mathematics & Economics 32(3): 345–358.CrossRefGoogle Scholar
6Chen, Y., Yuen, K.C., & Ng, K.W. (2011). Asymptotics for the ruin probabilities of a two-dimensional renewal risk model with heavy-tailed claims. Applied Stochastic Models in Business and Industry 27: 290–300.CrossRefGoogle Scholar
7Chen, Y., Wang, L., & Wang, Y. (2013). Uniform asymptotics for the finite-time ruin probabilities of two kinds of nonstandard bidimensional risk models. Journal of Mathematical Analysis and Applications 401: 114–129.CrossRefGoogle Scholar
8Chen, Y., Wang, Y., & Wang, K. (2013). Asymptotic results for ruin probability of a two-dimensional renewal risk model. Stochastic Analysis and Applications 31: 80–91.CrossRefGoogle Scholar
9Embrechts, P., Klüppelberg, C., & Mikosch, T. (1997). Modelling Extremal Events for Insurance and Finance. Berlin: Springer-Verlag.CrossRefGoogle Scholar
10Foss, S., Dmitry, K., Palmowski, S., & Rolski, T. (2017). Two-dimensional ruin probability for subexponential claim size. Probability and Mathematical Statistics 37(2): 319–335.Google Scholar
11Fu, K.A. (2016). On joint ruin probability for a bidimensional Lévy-driven risk model with stochastic returns and heavy-tailed claims. Journal of Mathematical Analysis and Applications 442: 17–30.CrossRefGoogle Scholar
12Gao, Q. & Yang, X. (2014). Asymptotic ruin probabilities in a generalized bidimensional risk model perturbed by diffusion with constant force of interest. Journal of Mathematical Analysis and Applications 419: 1193–1213.CrossRefGoogle Scholar
13Hao, X. & Tang, Q. (2008). A uniform asymptotic estimate for discounted aggregate claims with subexponential tails. Insurance Mathematics & Economics 43: 116–120.CrossRefGoogle Scholar
14Hu, Z. & Jiang, B. (2013). On joint ruin probabilities of a two-dimensional risk model with constant interest rate. Journal of Applied Probability 50(2): 309–322.CrossRefGoogle Scholar
15Jiang, T., Wang, Y., Chen, Y., & Xu, H. (2015). Uniform asymptotic estimate for finite-time ruin probabilities of a time-dependent bidimensional renewal model. Insurance Mathematics & Economics 64: 45–53.CrossRefGoogle Scholar
16Li, J., Tang, Q., & Wu, R. (2010). Subexponential tails of discounted aggregate claims in a time-dependent renewal risk model. Advances in Applied Probability 42(4): 1126–1146.CrossRefGoogle Scholar
17Tang, Q. & Tsitsiashvili, G. (2003). Precise estimates for the ruin probability in finite horizon in a discrete-time model with heavy-tailed insurance and financial risks. Stochastic Processes and their Applications 108(2): 299–325.CrossRefGoogle Scholar
18Tang, Q. & Yuan, Z. (2014). Randomly weighted sums of subexponential random variables with application to capital allocation. Extremes 17(3): 467–493.CrossRefGoogle Scholar
19Zhang, Y. & Wang, W. (2013). Ruin probabilities of a bidimensional risk model with constant interest rate. Journal of East China Normal University. Natural Science Edition 2013(6): 22–31.Google Scholar