# American Institute of Mathematical Sciences

January  2017, 13(1): 155-185. doi: 10.3934/jimo.2016010

## Asymptotics for ruin probabilities of a non-standard renewal risk model with dependence structures and exponential Lévy process investment returns

 1 School of Mathematical Sciences, School of Management and Economics, University of Electronic Science and Technology of China, Chengdu, 611731, China 2 School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731, China

* Corresponding author: Dingcheng Wang

Received  February 2015 Revised  December 2015 Published  March 2016

Fund Project: The research of Jiangyan Peng is supported by the National Natural Science Foundation of China (project no: 71501025) and China Postdoctoral Science Foundation (project no: 2015M572467). The research of Dingcheng Wang is supported by the National Natural Science Foundation of China (project no: 71271042).

Consider a non-standard renewal risk model with dependence structures, where claim sizes follow a one-sided linear process with independent and identically distributed step sizes, the step sizes and inter-arrival times respectively form a sequence of independent and identically distributed random pairs, with each pair obeying a dependence structure. An insurance company is allowed to make risk-free and risky investments, where the price process of the investment portfolio follows an exponential Lévy process. When the step-size distribution is dominatedly-varying-tailed, some asymptotic estimates for the finite-and infinite-time ruin probabilities are obtained.

Citation: Jiangyan Peng, Dingcheng Wang. Asymptotics for ruin probabilities of a non-standard renewal risk model with dependence structures and exponential Lévy process investment returns. Journal of Industrial & Management Optimization, 2017, 13 (1) : 155-185. doi: 10.3934/jimo.2016010
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