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Keywords = Tail Variance (TV)

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19 pages, 306 KiB  
Article
Asymptotic Tail Moments of the Time Dependent Aggregate Risk Model
by Dechen Gao and Jiandong Ren
Mathematics 2025, 13(7), 1153; https://doi.org/10.3390/math13071153 - 31 Mar 2025
Viewed by 161
Abstract
In this paper, we study an extension of the classical compound Poisson risk model with a dependence structure among the inter-claim time and the subsequent claim size. Under a flexible dependence structure and assuming that the claim amounts are heavy tail distributed, we [...] Read more.
In this paper, we study an extension of the classical compound Poisson risk model with a dependence structure among the inter-claim time and the subsequent claim size. Under a flexible dependence structure and assuming that the claim amounts are heavy tail distributed, we derive asymptotic tail moments for the aggregate claims. Numerical examples and simulation studies are provided to validate the results. Full article
(This article belongs to the Section D1: Probability and Statistics)
21 pages, 376 KiB  
Article
Tail Conditional Moments for Location-Scale Mixture of Elliptical Distributions
by Xiangyu Han and Chuancun Yin
Mathematics 2022, 10(4), 606; https://doi.org/10.3390/math10040606 - 16 Feb 2022
Cited by 3 | Viewed by 2008
Abstract
We present the general results on the univariate tail conditional moments for a location-scale mixture of elliptical distributions. Examples include the location-scale mixture of normal, location-scale mixture of Student’s t, location-scale mixture of logistic, and location-scale mixture of Laplace distributions. More specifically, [...] Read more.
We present the general results on the univariate tail conditional moments for a location-scale mixture of elliptical distributions. Examples include the location-scale mixture of normal, location-scale mixture of Student’s t, location-scale mixture of logistic, and location-scale mixture of Laplace distributions. More specifically, we give the tail variance, the tail conditional skewness, and the tail conditional kurtosis of generalised hyperbolic distribution and Student–GIG mixture distribution. We give an illustrative example, which discusses the TCE, TV, TCS and TCK of three stocks, including Amazon, Google and Apple. Full article
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