arXiv subjects

Dongya Cheng

Publications and source records attributed to Dongya Cheng.

4 recordsLinked to original sources

arXiv2025

Asymptotics of higher-order conditional tail moments for convolution-equivalently distributed losses

This paper investigates the asymptotic behavior of higher-order conditional tail moments, which quantify the contribution of individual losses in the event of systemic collapse. The study is conducted within a framework comprising two investment portfolios experiencing dependent losses that follow convolution-equivalent distributions. The main results are encapsulated in two theorems: one addressing light-tailed losses with convolution-equivalent distributions and the other focusing on heavy-tailed losses with regularly varying distributions. Both results reveal that the asymptotic behavior remains robust regardless of the strength of dependence. Additionally, numerical simulations are performed under specific scenarios to validate the theoretical results.

math.PR↗

arXiv2017

A necessary and sufficient condition for the subexponentiality of product distribution

Let X and Y be two independent and nonnegative random variables with corresponding distributions F and G. Denote by H the distribution of the product XY , called the product convolution of F and G. Cline and Samorodnitsky (1994) proposed sufficient conditions for H to be subexponential, given the subexponentiality of F. Relying on a related result of Tang (2008) on the long-tail of product convolution, we obtain a necessary and sufficient condition for the subexponentiality of H, given that of F. We also study the reverse problem and obtain sufficient conditions for the subexponentiality of F given that of H. Finally, we apply the obtained results to the asymptotic study of the ruin probability in a discrete-time insurance risk model with stochastic returns.

math.PR↗

arXiv2016

On closedness under convolution roots related to an infinitely divisible distribution in the distribution class L(γ)

We consider questions related to the well-known conjecture due to Embrechts and Goldie on the closedness of different classes of heavy- and light-tailed distributions with respect to convolution roots. We show that the class L(γ)\cap OS is not closed under convolution roots related to an infinitely divisible distribution for any γ\ge0, i.e. we provide examples of infinitely divisible distributions belonging to this class such that the corresponding Levy spectral distribution does not. We also prove a similar statement for the class (L(γ)\cap OS)\ S(γ). In order to facilitate our analysis, we explore the structural properties of some of the classes of distributions, and study some properties of the well-known transformation from a heavy-tailed distribution to a light-tailed one.

math.PR↗

arXiv2016

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 subexponential distribution. This distribution class and the corresponding generalized local subexponential distribution class are two new distribution classes with some good properties. Further, some long-tailed distributions with intuitive and concrete forms are found, which show that the intersection of the two above-mentioned distribution classes with long-tailed distribution class properly contain the strong subexponential distribution class and the locally subexponential distribution class, respectively.

math.PR↗