On domination problem of non-negative distributions

doi:10.1007/s11464-009-0040-6

Front. Math. China

2009, Vol. 4

Issue (4) : 681-696 https://doi.org/10.1007/s11464-009-0040-6

Research articles

On domination problem of non-negative distributions

Zishan SU,Chun SU,Zhishui HU,Jie LIU,

Department of Statistics and Finance, University of Science and Technology of China, Hefei 230026, China;

Download: PDF(181 KB)
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

Abstract The domination relationship between non-negative distributions is an important question in applied probability. It has important applications in the fields of finance, insurance and risk theory. In this paper, based on class "Graphic"

, we find the sufficient condition of dominating all light-tailed distributions and also discuss its necessity. Almost all heavy-tailed distributions often used in risk theory satisfy this condition. We also consider the domination problem between heavy-tailed distributions, and show that classes "Graphic"

 and "Graphic"

ℳ* have many good properties on domination problems.

Keywords [img]Non-negative distributions domination class class ℳ class  Karamata index

Issue Date: 05 December 2009

Cite this article:

Zishan SU,Chun SU,Zhishui HU, et al. On domination problem of non-negative distributions[J]. Front. Math. China, 2009, 4(4): 681-696.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-009-0040-6
https://academic.hep.com.cn/fmc/EN/Y2009/V4/I4/681

	Bingham N H, Goldie C M, Teugels J L. Regular Variation. Cambridge: Cambridge University Press, 1987
	Cheng Y B, Tang Q H, Yang H. Approximations for moments of deficit at ruin with exponentialand subexponential claims. Stat Prob Letters, 2002, 59(4): 367―378 doi: 10.1016/S0167-7152(02)00234-1
	Embrechts P, Klüppelberg C, Mikosch T. Modelling Extremal Events for Insuranceand Finance. Berlin: Springer, 1997
	Foss S, Korshunov D. Lower limits and equivalencesfor convolution tails. Ann Probab, 2007, 35(1): 366―383 doi: 10.1214/009117906000000647
	Greiner M, Jobmman M, Klüppelberg C. Telecommunication traffic, queueing modelsand subexponential distributions. QueueingSystems, 1999, 33: 125―152 doi: 10.1023/A:1019120011478
	Kalashinikov V. GeometricSums Bounds for Rare Events with Applications: Risk Analysis, Reliability,Queueing. Dordrecht: Kluwer Academic Publishers, 1997
	Mikosch T, Nagaev A. Rates in approximations toruin probabilities for heavy-tailed distributions. Extremes, 2001, 4(1): 67―78 doi: 10.1023/A:1012237524316
	Su C, Hu Z S, Chen Y, Liang H Y. A wide classof heavy-tailed distributions and its applications. Front Math China, 2007, 2(2): 257―286 doi: 10.1007/s11464-007-0018-1
	Su C, Hu Z S, Tang Q H. Characterizations on heaviness of distribution tailsof non-negative variables. Adv Math, 2003, 32(5): 606―614 (in Chinese)
	Su C, Tang Q H. Characterizations on heavy-taileddistributions by means of hazard rate. Acta Mathematicae Applicatae Sinica (English Ser), 2003, 19(1): 135―142 doi: 10.1007/s10255-003-0090-6
	Tang Q, Tsitsiashvili G. Precise estimates for theruin probability in finite horizon in a discrete-time model with heavy-tailedinsurance and financial risks. StochasticProcess Appl, 2003, 108(2): 299―325

[1]	Yu LI, Guiyun CHEN. Normalized integral table algebras generated by a faithful real element of degree 2 and having 4 linear elements[J]. Front. Math. China, 2019, 14(6): 1231-1258.
[2]	Jiajie HUA, Xiaochun FANG, Xiao-Ming XU. Continuity of functors with respect to generalized inductive limits[J]. Front. Math. China, 2019, 14(3): 551-566.
[3]	Yonggang HU, Hailou YAO. Relative homological dimensions in recollements of triangulated categories[J]. Front. Math. China, 2019, 14(1): 25-43.
[4]	Jiashun HU, Xiang MA, Chunxiong ZHENG. Global geometrical optics method for vector-valued Schrödinger problems[J]. Front. Math. China, 2018, 13(3): 579-606.
[5]	Yingying ZHANG,Zhaoyong HUANG. G-stable support τ-tilting modules[J]. Front. Math. China, 2016, 11(4): 1057-1077.
[6]	Yutao MA,Yingzhe WANG. Algebraic convergence of diffusion processes on Rn with radial diffusion and drift coefficients[J]. Front. Math. China, 2015, 10(4): 965-984.
[7]	Li-meng XIA,Naihong HU. A class of Lie algebras arising from intersection matrices[J]. Front. Math. China, 2015, 10(1): 185-198.
[8]	Lu QIU,Dianhua WU. Constructions of (q, K, λ, t, Q) almost difference families[J]. Front. Math. China, 2014, 9(2): 377-386.
[9]	Changjun YU,Yuebao WANG. Tail behavior of supremum of a random walk when Cramér’s condition fails[J]. Front. Math. China, 2014, 9(2): 431-453.
[10]	Zhangjia HAN, Guiyun CHEN, Huaguo SHI. On minimal non-I N I-groups[J]. Front Math Chin, 2013, 8(6): 1295-1306.
[11]	Mingchun XU. Thompson’s conjecture for alternating group of degree 22[J]. Front Math Chin, 2013, 8(5): 1227-1236.
[12]	Jixia YUAN, Wende LIU. Filtration, automorphisms, and classification of infinite-dimensional odd contact superalgebras[J]. Front Math Chin, 2013, 8(1): 203-216.
[13]	Futao HU, Jun-Ming XU. Bondage number of mesh networks[J]. Front Math Chin, 2012, 7(5): 813-826.
[14]	Nanying YANG, Wenbin GUO, N. T. VOROB’EV. Factorizations of Fitting classes[J]. Front Math Chin, 2012, 7(5): 943-954.
[15]	Xin ZHANG, Min SONG. Optimization of risk policy and dividends with fixed transaction costs under interest rate[J]. Front Math Chin, 2012, 7(4): 795-811.

Viewed

Full text

Abstract

Cited

Shared

Discussed