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Article
Closure under infinitely divisible distribution roots and the Embrechts–Goldie conjecture
We show that the distribution class ℒ(γ) \ 𝒪𝒮 is not closed under infinitely divisible distribution roots for γ > 0, that is, we provide some infinitely divisible distributions belonging to the class, whereas ...
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Article
Open AccessDividend and Capital Injection Optimization with Transaction Cost for Lévy Risk Processes
The optimal dividends problem has remained an active research field for decades. For an insurance company with reserve modelled by a spectrally negative Lévy process having finite first-order moment, we study ...
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Article
On the closure under infinitely divisible distribution roots
For some γ > 0, we show that the distribution class (ℒ(γ) ∩𝒪S)\S(γ) is not closed under infinitely divisible distribution roots, that is, we provide examples showing that some infinitely divisible distributions b...
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Article
On the long tail property of product convolution
Let X and Y be two independent random variables with corresponding distributions F and G on [0,∞). The distribution of the product XY , which is called the product convolution of F and G, is denoted by H. In this...
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Article
Asymptotics of convolution with the semi-regular-variation tail and its application to risk
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 cal...
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Article
The local asymptotic estimation for the supremum of a random walk with generalized strong subexponential summands
In this paper, the local asymptotic estimation for the supremum of a random walk and its applications are presented. The summands of the random walk have common long-tailed and generalized strong subexponentia...
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Article
An inequality of widely dependent random variables and its applications*
In this paper, we prove a more accurate inequality of widely dependent random variables. Based on this inequality, we obtain some limit theorems for widely dependent random variables, which expand ranges of do...
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Article
Convolution and convolution-root properties of long-tailed distributions
We obtain a number of new general properties, related to the closedness of the class of long-tailed distributions under convolutions, that are of interest themselves and may be applied in many models that deal...
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Article
Tail behavior of the sums of dependent and heavy-tailed random variables
In this paper, we investigate the tail asymptotic behavior of the partial sums, the random sums and the weighted sums of heavy-tailed random variables (r.v.s.) under two new dependence structures, respectively...
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Article
Tail behavior of supremum of a random walk when Cramér’s condition fails
We investigate tail behavior of the supremum of a random walk in the case that Cramér’s condition fails, namely, the intermediate case and the heavy-tailed case. When the integrated distribution of the increme...
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Article
Almost sure asymptotics for extremes of non-stationary Gaussian random fields
In this paper, the authors prove an almost sure limit theorem for the maxima of non-stationary Gaussian random fields under some mild conditions related to the covariance functions of the Gaussian fields. As t...
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Article
On asymptotic equivalence among the solutions of some defective renewal equations
We obtain some sufficient conditions for mutually asymptotic equivalence among solutions of some defective renewal equations, where the related distributions can be heavy-tailed but are not required to be sube...
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Article
Uniform Asymptotics for the Finite-Time Ruin Probability of a Dependent Risk Model with a Constant Interest Rate
This paper gives an asymptotically equivalent formula for the finite-time ruin probability of a nonstandard risk model with a constant interest rate, in which both claim sizes and inter-arrival times follow a ...
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Article
Tail behavior of the product of two dependent random variables with applications to risk theory
Let the random vector (X,Y) follow a bivariate Sarmanov distribution, where X is real-valued and Y is nonnegative. In this paper we investigate the impact of such a dependence structure between X and Y on the tai...
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Article
Some properties of the exponential distribution class with applications to risk theory
This paper derives some equivalent conditions for tail equivalence of a distribution G and the convolution G*H, where G belongs to the exponential distribution class and H is another distribution. This generalize...
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Article
Some asymptotic results on extremes of incomplete samples
Let X 1,X 2, ⋯ be a sequence of independent and identically distributed random variables and M n = max {X 1,X ...
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Article
Ruin probabilities with pairwise quasi-asymptotically independent and dominatedly-varying tailed claims
This paper considers the nonstandard renewal risk model in which a part of surplus is invested into a Black-Scholes market whose price process is modelled by a geometric Brownian motion, claim sizes form a seq...
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Article
Asymptotic behavior of the ratio of tail probabilities of sum and maximum of independent random variables
For a fixed integer n ≥ 2, let X 1 ,…, X n be independent random variables (r.v.s) with distributions F 1,…,F ...
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Article
Almost sure central limit theorem for the maxima and sums of stationary Gaussian sequences
In this paper, we proved an almost sure central limit theorem for the maxima (after centered at the sample mean) and the partial sums of standardized stationary Gaussian sequences under some conditions related...
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Article
Open AccessOn the exponential inequality for acceptable random variables
In this paper, we obtain some new exponential inequalities for partial sums and their finite maximum of acceptable random variables by the results of Sung et al. (J. Korean Stat. Soc., 40, 109-114, 2011) and i...
