[1] Yang Yang, Liu Wei, Lin Jinguan, et al. Uniform asymptotics for finite-time ruin probability in somedependent compound risk models with constant interest rate [J]. Journal of Southeast University (English Edition), 2014, 30 (1): 118-121. [doi:10.3969/j.issn.1003-7985.2014.01.022]

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Uniform asymptotics for finite-time ruin probability in somedependent compound risk models with constant interest rate()

带有常数利息率的相依复合风险模型中有限时破产概率的一致渐近性

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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

30

Issue:

2014 1

Page:

118-121

Research Field:

Mathematics, Physics, Mechanics

Publishing date:

2014-03-31

Info

Title:

Uniform asymptotics for finite-time ruin probability in somedependent compound risk models with constant interest rate

带有常数利息率的相依复合风险模型中有限时破产概率的一致渐近性

Author(s):

Yang Yang^{1, 2}, Liu Wei³, Lin Jinguan⁴, Zhang Yulin¹

¹School of Economics and Management, Southeast University, Nanjing 210096, China
²School of Mathematics and Statistics, Nanjing Audit University, Nanjing 210029, China
³College of Mathematics and System Science, Xinjiang University, Urumqi 830046, China
⁴Department of Mathematics, Southeast University, Nanjing 210096, China

杨洋^{1, 2}, 刘伟³, 林金官⁴, 张玉林¹

¹东南大学经济管理学院, 南京 210096; ²南京审计学院数学与统计学院, 南京 210029; ³新疆大学数学与系统科学学院, 乌鲁木齐 830046; ⁴东南大学数学系, 南京 210096

Keywords:

compound and non-compound risk models;  finite-time ruin probability;  dominatedly varying tail;  uniform asymptotics;  random sums;  dependence structure

复合及非复合风险模型;  有限时破产概率;  控制变换尾;  一致渐近性;  随机和;  相依结构

PACS:

O211.4

DOI:

10.3969/j.issn.1003-7985.2014.01.022

Abstract:

Consider two dependent renewal risk models with constant interest rate. By using some methods in the risk theory, uniform asymptotics for finite-time ruin probability is derived in a non-compound risk model, where claim sizes are upper tail asymptotically independent random variables with dominatedly varying tails, claim inter-arrival times follow the widely lower orthant dependent structure, and the total amount of premiums is a nonnegative stochastic process. Based on the obtained result, using the method of analysis for the tail probability of random sums, a similar result in a more complex and reasonable compound risk model is also obtained, where individual claim sizes are specialized to be extended negatively dependent and accident inter-arrival times are still widely lower orthant dependent, and both the claim sizes and the claim number have dominatedly varying tails.

考虑了2个带有常数利息率的相依更新风险模型.首先研究了非复合风险模型, 其中索赔额是上尾渐近独立且带有控制变换尾分布的非负随机变量, 索赔时间间隔是宽下象限相依的, 保费收入过程是一个非负的随机过程, 利用风险理论中的方法, 得到了有限时破产概率在某个有界区间上的一致渐近性.在此基础上, 利用随机和尾渐近性的分析方法, 进一步研究获得了更为复杂且合理的复合相依更新风险模型中有限时破产概率的一致渐近性公式, 其中单个索赔额特殊化为广义负相依的, 并且事故时间间隔仍然保持宽下象限相依的, 索赔额和索赔次数均为控制变换尾的.

References:

[1] Tang Q H, Su C, Jiang T, et al. Large deviations for heavy-tailed random sums in compound renewal model [J]. Statist Prob Lett, 2001, 52(1): 91-100.
[2] Maulik K, Resnick S. Characterizations and examples of hidden regular variation [J]. Extremes, 2004, 7(1): 31-67.
[3] Wang K Y, Wang Y B, Gao Q W. Uniform asymptotics for the finite-time ruin probability of a dependent risk model with a constant interest rate [J]. Methodol Comput Appl Prob, 2013, 15(1): 109-124.
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[5] Tang Q H. Heavy tails of discounted aggregate claims in the continuous-time renewal model [J]. J Appl Prob, 2007, 44(2): 285-294.
[6] Yang Y, Wang Y B, Leipus R, et al. Asymptotics for tail probability of total claim amount with negatively dependent claim sizes and its applications [J]. Lith Math J, 2009, 49(3): 337-352.
[7] Yang Y, Lin J G, Huang C, et al. The finite-time ruin probability in two nonstandard renewal risk models with constant interest rate and dependent subexponential claims [J]. J Korean Statist Society, 2012, 41(2): 213-224.
[8] Yang Y, Wang K Y, Liu J. Asymptotics and uniform asymptotics for finite-time and infinite-time absolute ruin probabilities in a dependent compound renewal risk model [J]. J Math Anal Appl, 2013, 398(1): 352-361.
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Memo

Memo:

Biography: Yang Yang(1979—), male, doctor, associate professor, yyangmath@gmail.com.
Foundation items: The National Natural Science Foundation of China(No. 11001052, 11171065, 71171046), China Postdoctoral Science Foundation(No. 2012M520964), the Natural Science Foundation of Jiangsu Province(No. BK20131339), the Qing Lan Project of Jiangsu Province.
Citation: Yang Yang, Liu Wei, Lin Jinguan, et al. Uniform asymptotics for finite-time ruin probability in some dependent compound risk models with constant interest rate[J].Journal of Southeast University(English Edition), 2014, 30(1):118-121.[doi:10.3969/j.issn.1003-7985.2014.01.022]

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