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