A NECESSARY AND SUFFICIENT CONDITION FOR THE SUBEXPONENTIALITY OF THE PRODUCT CONVOLUTION

作者：Xu, Hui; Cheng, Fengyang; Wang, Yuebao^*; Cheng, Dongya

来源：Advances in Applied Probability, 2018, 50(1): 57-73.

DOI：10.1017/apr.2018.4

• Necessary and sufficient condition
• product convolution
• subexponential distribution
• discrete-time insurance risk model

Let X and Y be two independent and nonnegative random variables with corresponding distributions F and G. Denote by H the distribution of the product XY, called the product convolution of F and G. Cline and Samorodnitsky (1994) proposed sufficient conditions for H to be subexponential, given the subexponentiality of F. Relying on a related result of Tang (2008) on the long-tail of the product convolution, we obtain a necessary and sufficient condition for the subexponentiality of H, given that of F. We also study the reverse problem and obtain sufficient conditions for the subexponentiality of F, given that of H. Finally, we apply the obtained results to the asymptotic study of the ruin probability in a discrete-time insurance risk model with stochastic returns.

• 出版日期2018-3
• 单位苏州大学