[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()

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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

Author(s):

Yang Yang¹;  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

Keywords:

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

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.

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.
[4] Liu L. Precise large deviations for dependent random variables with heavy tails [J]. Statist Prob Lett, 2009, 79(9): 1290-1298.
[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.
[9] Yi L, Chen Y, Su C. Approximation of the tail probability of randomly weighted sums of dependent random variables with dominated variation [J]. J Math Anal Appl, 2011, 376(1): 365-372.
[10] Yang Y, Wang K Y. Precise large deviations for dependent random variables with applications to the compound renewal risk model [J]. Rocky Moun J Math, 2013, 43(4): 1395-1414.
[11] Chen Y, Chen A, Ng K W. The strong law of large numbers for extend negatively dependent random variables [J]. J Appl Prob, 2010, 47(4): 908-922.

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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