A necessary and sufficient condition for the subexponentiality of product distribution

2016/05/08 by Hui Xu, Fengyang Cheng, Xu, Hui +5
Decision Sciences · Economics, Econometrics and Finance · Social Sciences · #60E05 #60G50 #62E20 #FOS: Mathematics #Financial Risk and Volatility Modeling #Insurance, Mortality, Demography, Risk Management #Probability (math.PR) #Probability and Risk Models

paper · pdf · doi:10.48550/arxiv.1605.02319

openalex publication_date 2016/05/08 · openalex created_date 2016/08/23 · openalex updated_date 2026/07/28

Abstract

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 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.

Citations

• Subexponentiality of the product of independent random variables
• On Some Limit Theorems Similar to the Arc-Sin Law

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