一类带有宽负相依索赔额的新风险模型损失过程的精细大偏差
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摘要
本文研究一类基于保单进入过程的风险模型,客户在其保期内可索赔多次.假设每个顾客的索赔额是宽负相依的且服从重尾分布,不同顾客之间的索赔额是相互独立的.本文得到了损失过程的大偏差.
This paper considers a risk model based on the policy entrance process, in which each customer is allowed to claim more than once within the validity time. The claim sizes caused by each customer are described as extended negatively dependent distributed heavy-tailed random variables, and claims due to different customers are independent and identically distributed heavy-tailed random variables. We derive the large deviations for the loss process of the risk model.
This paper considers a risk model based on the policy entrance process, in which each customer is allowed to claim more than once within the validity time. The claim sizes caused by each customer are described as extended negatively dependent distributed heavy-tailed random variables, and claims due to different customers are independent and identically distributed heavy-tailed random variables. We derive the large deviations for the loss process of the risk model.
引文
[1] Li Z H, Kong X B. A new risk model based on policy entrance process and its weak convergence properties. Appl. Stoch. Model. Bus.,2007, 3(23):235-246
[2] Chen Y, Ng K W. The ruin probability of the renewal model with constant interest force and negatively dependent heavy-tailed claims. Insur. Math. Econ., 2007, 40(3):415-423
[3]杨洋,林金官,高庆武·时间相依更新风险模型中无限时绝对破产概率的渐近性.中国科学:数学,2013,2(43):173-184(Yang Y, Lin J G, Gao Q W. Asymptotics for the infinite-time absolute ruin probabilities in timedependent renewal risk models. Sci. China. Math., 2013, 2(43):173-184)
[4] Liu X J, Yu C J, Gao Q W. Precise large deviations of aggregate claim amount in a dependent renewal risk model. Commun. Stat-Theor. M., 2017, 5(46):2354-2363
[5] Kliippelberg C, Mikosch T. Large deviations of heavy-tailed random sums with applications in insurance and finance. J. Appl. Probab.,1997, 34(2):293-308
[6] Mikosch T, Nagaev A V. Large deviations heavy-tailed sums with applications in insurance. Extremes,1998, 1(1):81-110
[7] Tang Q. Insensitivity to negative dependence of the asymptotic behavior of precise large deviations.Electron. J. Probab., 2006, 11:107-120
[8] Chen Y, Zhang W P. Large deviations for random sums of negatively dependent random variables with consistently varying tails. Stat. Probabil. Lett.,2007, 5(77):530-538
[9] Chen Y Q, Yuen K C, Ng K W. Precise Large Deviations of Random Sums in Presence of Negative Dependence and Consistent Variation. Methodol. Comput. Appl.,2011, 13(4):821-833
[10] Liu L. Precise large deviations for dependent random variables with heavy tails. Stat. Probabil. Lett.,2009, 79(9):1290-1298
[11] Ng K, Tang Q, Yan J, Yang H. Precise large deviations for sums of random variables with consistently varying tails. J. Appl. Probab.,2004, 1(41):93-107
[12] Tang Q. Insensitivity to negative dependence of asymptotic tail probabilities of sums and maxima of sums. Stoch. Anal. Appl.,2008, 3(26):435-450
[13] Tang Q, Su Q, Jiang T, Zhang J. Large deviations for heavy-tailed random sums in compound renewal model. Stat. Probabil. Lett., 2001, 1(52):91-100
[14] Tang F, Bai J. Precise large deviations for aggregate loss process in a multi-risk model. J. Koren.Math. Soc., 2015, 52(3):447-467
[15] Wang D, Tang Q. Maxima of sums and random sums for negatively associated random variables with heavy tails. Stat. Probabil. Lett., 2004, 3(68):287-295
[16] Kaas R, Tang Q. A large deviation result for aggregate claims with dependent claim occurrences.Insur. Math. Econom.,2005, 3(36):251-259
[2] Chen Y, Ng K W. The ruin probability of the renewal model with constant interest force and negatively dependent heavy-tailed claims. Insur. Math. Econ., 2007, 40(3):415-423
[3]杨洋,林金官,高庆武·时间相依更新风险模型中无限时绝对破产概率的渐近性.中国科学:数学,2013,2(43):173-184(Yang Y, Lin J G, Gao Q W. Asymptotics for the infinite-time absolute ruin probabilities in timedependent renewal risk models. Sci. China. Math., 2013, 2(43):173-184)
[4] Liu X J, Yu C J, Gao Q W. Precise large deviations of aggregate claim amount in a dependent renewal risk model. Commun. Stat-Theor. M., 2017, 5(46):2354-2363
[5] Kliippelberg C, Mikosch T. Large deviations of heavy-tailed random sums with applications in insurance and finance. J. Appl. Probab.,1997, 34(2):293-308
[6] Mikosch T, Nagaev A V. Large deviations heavy-tailed sums with applications in insurance. Extremes,1998, 1(1):81-110
[7] Tang Q. Insensitivity to negative dependence of the asymptotic behavior of precise large deviations.Electron. J. Probab., 2006, 11:107-120
[8] Chen Y, Zhang W P. Large deviations for random sums of negatively dependent random variables with consistently varying tails. Stat. Probabil. Lett.,2007, 5(77):530-538
[9] Chen Y Q, Yuen K C, Ng K W. Precise Large Deviations of Random Sums in Presence of Negative Dependence and Consistent Variation. Methodol. Comput. Appl.,2011, 13(4):821-833
[10] Liu L. Precise large deviations for dependent random variables with heavy tails. Stat. Probabil. Lett.,2009, 79(9):1290-1298
[11] Ng K, Tang Q, Yan J, Yang H. Precise large deviations for sums of random variables with consistently varying tails. J. Appl. Probab.,2004, 1(41):93-107
[12] Tang Q. Insensitivity to negative dependence of asymptotic tail probabilities of sums and maxima of sums. Stoch. Anal. Appl.,2008, 3(26):435-450
[13] Tang Q, Su Q, Jiang T, Zhang J. Large deviations for heavy-tailed random sums in compound renewal model. Stat. Probabil. Lett., 2001, 1(52):91-100
[14] Tang F, Bai J. Precise large deviations for aggregate loss process in a multi-risk model. J. Koren.Math. Soc., 2015, 52(3):447-467
[15] Wang D, Tang Q. Maxima of sums and random sums for negatively associated random variables with heavy tails. Stat. Probabil. Lett., 2004, 3(68):287-295
[16] Kaas R, Tang Q. A large deviation result for aggregate claims with dependent claim occurrences.Insur. Math. Econom.,2005, 3(36):251-259