Asymptotics of convolution with the semi-regular-variation tail and its application to risk |
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Authors: | Zhaolei Cui Edward Omey Wenyuan Wang Yuebao Wang |
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Institution: | 1.School of Mathematics and Statistics,Changshu Institute of Technology,Suzhou,People’s Republic of China;2.Faculty of Economics and Business-Campus Brussels,KU Leuven,Brussels,Belgium;3.School of Mathematical Sciences,Xiamen University,Xiamen,People’s Republic of China;4.School of Mathematical Sciences,Soochow University,Suzhou,People’s Republic of China |
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Abstract: | In this paper, according to a certain criterion, we divide the exponential distribution class into some subclasses. One of them is closely related to the regular-variation-tailed distribution class, and is called the semi-regular-variation-tailed distribution class. The new class possesses several nice properties, although distributions in it are not convolution equivalent. We give the precise tail asymptotic expression of convolutions of these distributions, and prove that the class is closed under convolution. In addition, we do not need to require the corresponding random variables to be identically distributed. Finally, we apply these results to a discrete time risk model with stochastic returns, and obtain the precise asymptotic estimation of the finite time ruin probability. |
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