Uniform Estimate for Maximum of Randomly Weighted Sums with Applications to Ruin Theory

A Note on the Tail Behavior of Randomly Weighted Sums with Convolution-Equivalently Distributed Random Variables

“…Many works have considered the heavytailed case; that is, the distribution of belongs to some classes of heavy-tailed distributions, even under some dependence structures. For example, one can refer to Tang and Tsitsiashvili [2,3], Wang and Tang [4], Zhang et al [5], Shen et al [6], Chen and Yuen [7], Gao and Wang [8], and Yi et al [9] among others for some details in this direction, where the distribution is heavily heavy tailed; as for some lightly heavy-tailed distribution , some related results were obtained by Tang and Tsitsiashvili [3,10], Chen and Su [11], Hashorva et al [12], Yang et al [13], Yang and Hashorva [14], and Yang and Wang [15] among others. We pointed out that Tang and Tsitsiashvili [3] achieved some interesting results on the asymptotics for the tail probability P( > ) in some cases where belongs to the intersection between the subexponential distribution class and the rapidly varying distribution class.…”

Asymptotic Tail Probability of Randomly Weighted Sum of Dependent Heavy-Tailed Random Variables

“…While F belongs to some wider class of heavy-tailed distribution, such as the intersection of the long-tailed and dominant variation class and subexponential class, the asymptotic result (1.1) holds when more stronger conditions on the random weights {Θ i , i ≥ 1} are imposed, see Tang andTsitsiashvili (2003, 2004), Wang and Tang (2006), Chen and Su (2006). When random variables X 1 , · · · , X n are not independent but identical, Zhang et al (2009) proved that the relation (1.1) holds when F belongs to an extended regular variation class which is a subclass of subexponential class; Shen et al (2009) obtained a uniform estimate for the maximum sums of uppertail independent and heavytailed random variables with non-negative dependent random weights.…”

Approximation of the Tail Probabilities for Bidimensional Randomly Weighted Sums With Dependent Components

“…In recent decades, analysis of the problem of approximating the tail probabilities P(S n > x) and P(M n > x) has been an attractive research topic in the literature on applied probability due to their practical importance; see Tang and Tsitsiashvili [17], Chen et al [2], Shen et al [16], Zhang et al [22], Gao and Wang [6], Hazra and Maulik [7], Olvera-Cravioto [14], and Tang and Yuan [19], among others. Notably, in all these references, the authors aim to show that the relations…”