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Uniform Estimate for Randomly Weighted Sums of Dependent Subexponential Random Variables

Author

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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)

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.

Suggested Citation

  • Liu Yan & Zhang Qinqin, 2015. "Uniform Estimate for Randomly Weighted Sums of Dependent Subexponential Random Variables," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 9(2), pages 303-318, July.
    • Handle: RePEc:bpj:apjrin:v:9:y:2015:i:2:p:303-318:n:1
    DOI: 10.1515/apjri-2014-0018
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    References listed on IDEAS

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    1. Chen Yu & Zhang Weiping & Liu Jie, 2010. "Asymptotic Tail Probability of Randomly Weighted Sum of Dependent Heavy-Tailed Random Variables," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 4(2), pages 1-11, July.
    2. Xin-mei Shen & Zheng-yan Lin & Yi Zhang, 2009. "Uniform Estimate for Maximum of Randomly Weighted Sums with Applications to Ruin Theory," Methodology and Computing in Applied Probability, Springer, vol. 11(4), pages 669-685, December.
    3. Zhang, Yi & Shen, Xinmei & Weng, Chengguo, 2009. "Approximation of the tail probability of randomly weighted sums and applications," Stochastic Processes and their Applications, Elsevier, vol. 119(2), pages 655-675, February.
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