A necessary and sufficient condition for the subexponentiality of the product convolution

Autor:	Hui Xu, Fengyang Cheng, Yuebao Wang, Dongya Cheng
Rok vydání:	2018
Předmět:	Statistics and Probability Applied Mathematics 010102 general mathematics 01 natural sciences Convolution 010104 statistics & probability Risk model Distribution (mathematics) Product (mathematics) Applied mathematics 0101 mathematics Cline (hydrology) Random variable Mathematics
Zdroj:	Advances in Applied Probability. 50:57-73
ISSN:	1475-6064 0001-8678
DOI:	10.1017/apr.2018.4
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::0f9a0dedd5a8c0c7771f946fa4b6126a https://doi.org/10.1017/apr.2018.4 Zobrazit plný text záznamu