常利息力下非标准连续时间更新风险模型破产概率的渐近性态
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摘要
讨论一个非标准连续时间更新风险模型,其中理赔变量序列为一列两两尾拟渐近独立(TQAI)非负随机变量,在常数利息力假定下,得到了其有限时间破产概率的渐近估计式,并进一步讨论了估计的一致性,推广了[1,2,8]等文献的结果.
A nonstandard continuous-time renewal risk model is discussed,in which the claim sequence is assumed to be a sequence of pairwise tail quasi-asymptotically independent(TQAI)random variables.Under the constant interest force,the asymptotic approximation of finite-time ruin probability for such a model is investigated.Furthermore,the uniformity of such an approximation is also discussed.The obtained result extends some existing ones in [1,2,8] and so on.
A nonstandard continuous-time renewal risk model is discussed,in which the claim sequence is assumed to be a sequence of pairwise tail quasi-asymptotically independent(TQAI)random variables.Under the constant interest force,the asymptotic approximation of finite-time ruin probability for such a model is investigated.Furthermore,the uniformity of such an approximation is also discussed.The obtained result extends some existing ones in [1,2,8] and so on.
引文
[1]Chen Y Q,Ng K W.The ruin probability of the renewal model with constant interest force and negatively dependent heavy-tailed claims[J].Insurance Mathematics and Economics,2007,40:415-423.
[2]Tang Q H.Heavy tails of discounted aggregate claims in the continuous-time renewal model[J].Journal of Applied Probability,2007,44:285-294.
[3]Shen X M,Lin Z Y.The ruin probability of renewal model with constant interest force and upper-tailed independent heavy-tailed claims[J].Acta Mathematica Sinica,English Series,2010,26(9):1815-1826.
[4]Sundt B,Teugels J L.Ruin estimates under interest force[J].Insurance Mathematics and Economics,1995,16:7-22.
[5]Klüppelberg C,Stadtmüller U.Ruin probabilities in the presence of heavy-tails and interest rates[J].Scandinavian Actuarial Journal,1998(1):49-58.
[6]Tang Q H.The finite-time ruin probability of the compound Poisson model with constant interest force[J].Journal of Applied Probability,2005,42:608-619.
[7]Cheng D Y.Random weighted sums of dependent random variables with dominated variation[J].Journal of Mathematical Analysis and Applications,2014,420:1617-1633.
[8]Shen X M,Lin Z Y,Zhang Y.Uniform estimate for maximum of randomly weighted sums with applications to ruin probability[J].Methodology and Computing in Applied Probability,2009,11(4):669-685.
[9]孔繁超,曹龙,王金亮.复合更新风险模型下的破产概率[J].大学数学,2005,21(3):6-12.
[10]向阳,刘再明.保费收入为Poisson过程的更新风险模型[J].大学数学,2007,23(1):26-28.
[11]Chen Y Q,Yuen K.Sums of pairwise quasi-Asymptotically independent random variables with consistent variation[J].Stochastic Models,2009,25(1):76-89.
[12]Kotz S,Balakrishnan N,Johnson N L.Continuous multivariate distributions[M].New York:Wiley-Interscience,2000.
[13]Embrechts P,Klüppelberg C,Mikosch T.Modelling Extremal Events for Insurance and Finance[M].Berlin:Springer,Heidelberg,1997.
[14]Bingham N H,Goldie C M,Teugels J L.Regular Variation[M].Cambridge:Cambridge University Press,1987.
[2]Tang Q H.Heavy tails of discounted aggregate claims in the continuous-time renewal model[J].Journal of Applied Probability,2007,44:285-294.
[3]Shen X M,Lin Z Y.The ruin probability of renewal model with constant interest force and upper-tailed independent heavy-tailed claims[J].Acta Mathematica Sinica,English Series,2010,26(9):1815-1826.
[4]Sundt B,Teugels J L.Ruin estimates under interest force[J].Insurance Mathematics and Economics,1995,16:7-22.
[5]Klüppelberg C,Stadtmüller U.Ruin probabilities in the presence of heavy-tails and interest rates[J].Scandinavian Actuarial Journal,1998(1):49-58.
[6]Tang Q H.The finite-time ruin probability of the compound Poisson model with constant interest force[J].Journal of Applied Probability,2005,42:608-619.
[7]Cheng D Y.Random weighted sums of dependent random variables with dominated variation[J].Journal of Mathematical Analysis and Applications,2014,420:1617-1633.
[8]Shen X M,Lin Z Y,Zhang Y.Uniform estimate for maximum of randomly weighted sums with applications to ruin probability[J].Methodology and Computing in Applied Probability,2009,11(4):669-685.
[9]孔繁超,曹龙,王金亮.复合更新风险模型下的破产概率[J].大学数学,2005,21(3):6-12.
[10]向阳,刘再明.保费收入为Poisson过程的更新风险模型[J].大学数学,2007,23(1):26-28.
[11]Chen Y Q,Yuen K.Sums of pairwise quasi-Asymptotically independent random variables with consistent variation[J].Stochastic Models,2009,25(1):76-89.
[12]Kotz S,Balakrishnan N,Johnson N L.Continuous multivariate distributions[M].New York:Wiley-Interscience,2000.
[13]Embrechts P,Klüppelberg C,Mikosch T.Modelling Extremal Events for Insurance and Finance[M].Berlin:Springer,Heidelberg,1997.
[14]Bingham N H,Goldie C M,Teugels J L.Regular Variation[M].Cambridge:Cambridge University Press,1987.