Uniform Estimate for Randomly Weighted Sums of Dependent Subexponential Random Variables

Liu Yan () and Zhang Qinqin ()
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Liu Yan: School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei 430072, P.R. China
Zhang Qinqin: School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei 430072, P.R. China

Asia-Pacific Journal of Risk and Insurance, 2015, vol. 9, issue 2, 303-318

Abstract: This paper obtains the uniform tail asymptotics of the maximum of randomly weighted sum max1≤k≤n∑i=1kθiXi$$\mathop {\max}\limits_{1 \le k \le n} \sum\nolimits_{i = 1}^k {\theta _i}{X_i}$$ with respective to n, in which the primary random variables X1,...,Xn$${X_1},...,{X_n}$$ are real valued, dependent, and have different subexponential distributions, while the random weights θ1,...,θn$${\theta _1},...,{\theta _n}$$ are nonnegative and arbitrarily dependent, but independent of X1,...,Xn$${X_1},...,{X_n}$$. An application to insurance risk model with investment portfolio is proposed.

Keywords: uniform asymptotics; subexponential distributions; Ruin probability; insurance risk; investment portfolio; Primary 62P05; Secondary 62E20; 91B30 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1515/apjri-2014-0018

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