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April  2017, 13(2): 995-1007. doi: 10.3934/jimo.2016058

## Infinite-time ruin probability of a renewal risk model with exponential Levy process investment and dependent claims and inter-arrival times

 1 School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China 2 Center of Financial Engineering, Nanjing Audit University, Nanjing 211815, China

* Corresponding author

Received  December 2015 Revised  June 2016 Published  August 2016

We investigate the infinite-time ruin probability of a renewal risk model with exponential Lévy process investment and dependent claims and inter-arrival times. Assume that claims and corresponding inter-arrival times form a sequence of independent and identically distributed copies of a random pair $(X,T)$ with dependent components. When the product of the claims and the discount factors of the corresponding inter-arrival times are heavy tailed, we establish an asymptotic formula for the infinite-time ruin probability without any restriction on the dependence structure of $(X,T)$.

Citation: Rongfei Liu, Dingcheng Wang, Jiangyan Peng. Infinite-time ruin probability of a renewal risk model with exponential Levy process investment and dependent claims and inter-arrival times. Journal of Industrial & Management Optimization, 2017, 13 (2) : 995-1007. doi: 10.3934/jimo.2016058
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##### References:
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