带布朗扰动风险模型的有限时破产概率渐近性（英文）
|
摘要
考虑了一个带有常利率和布朗扰动的一般风险模型,这种风险模型不需要假设索赔来到时间间隔独立或者相依.当索赔额具有WUOD相依结构并且属于重尾分布族时,就得到了有限时破产概率的渐近表达式,这意味着布朗扰动对于有限时破产概率的渐近性没有影响.
In this paper,a general risk model with constant force of interest and Brownian perturbation is considered.It does not need independent or dependent assumption on the inter-arrival times in this risk model.When the claim sizes are WUOD and have heavy-tailed distributions,the asymptotics of the finite-time ruin probability have been obtained,which shows that the Brownian perturbation has no effect on the asymptotics of the finite-time ruin probability.
In this paper,a general risk model with constant force of interest and Brownian perturbation is considered.It does not need independent or dependent assumption on the inter-arrival times in this risk model.When the claim sizes are WUOD and have heavy-tailed distributions,the asymptotics of the finite-time ruin probability have been obtained,which shows that the Brownian perturbation has no effect on the asymptotics of the finite-time ruin probability.
引文
[1] KlPPELBERG C. Subexponential distribution and integrated tails[J].Journal of Applied Probability,1998,25(1):132-141.
[2] EMBRECHTS P, KlPPELBERG C, MIKOSCH T.Modelling Extremal Events for Insurance and Finance[M].Berlin:Springer,1997.
[3] FOSS S,KORSHUNOV D,ZACHARY S.An Introduction to Heavy-tailed and Subexponential Distribution[M].2nd Ed.New York:Springer,2013.
[4] 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].Methodology&Computing in Applied Probability,2013,15(1):109-124.
[5] EBRAHIMI N, GHOSH M. Multivariate negative dependence[J].Communication in Statistics-Theory and Methods,1981,1030(4):7-337.
[6] BLOCK H W,SAVITS T H,SHAKED M.Some concepts of negative dependence[J].The Annals of Probability,1982,10(3):765-772.
[7] LIU L.Precise large deviations for dependent random variables with heavy tails[J].Statistics&Probability Letters,2009,79(9):1290-1298.
[8] MAO Y Z,WANG K Y,ZHU L,et al.Asymptotics for the finite-time ruin probability of a risk model with a general counting process[J].Japan Journal of Industrial and Applied,2017,34(1):243-252.
[9] ROGOZIN B A,SGIBNEV M S. Banach algebras of measures on the line with given asymptotics of distrbutions at infinity[J].Siberian Mathematical Journal,1999,40(3):565-576.
[2] EMBRECHTS P, KlPPELBERG C, MIKOSCH T.Modelling Extremal Events for Insurance and Finance[M].Berlin:Springer,1997.
[3] FOSS S,KORSHUNOV D,ZACHARY S.An Introduction to Heavy-tailed and Subexponential Distribution[M].2nd Ed.New York:Springer,2013.
[4] 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].Methodology&Computing in Applied Probability,2013,15(1):109-124.
[5] EBRAHIMI N, GHOSH M. Multivariate negative dependence[J].Communication in Statistics-Theory and Methods,1981,1030(4):7-337.
[6] BLOCK H W,SAVITS T H,SHAKED M.Some concepts of negative dependence[J].The Annals of Probability,1982,10(3):765-772.
[7] LIU L.Precise large deviations for dependent random variables with heavy tails[J].Statistics&Probability Letters,2009,79(9):1290-1298.
[8] MAO Y Z,WANG K Y,ZHU L,et al.Asymptotics for the finite-time ruin probability of a risk model with a general counting process[J].Japan Journal of Industrial and Applied,2017,34(1):243-252.
[9] ROGOZIN B A,SGIBNEV M S. Banach algebras of measures on the line with given asymptotics of distrbutions at infinity[J].Siberian Mathematical Journal,1999,40(3):565-576.