利率和利息力因素下的风险模型
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摘要
在市场经济中,一切经济活动都在受着利率的影响,保险业也不例外.再加上保险本身就是一项有风险的活动,所以如何更好的规避风险,稳定经营,就成了保险公司最关心的问题.由此,学者也在逐渐探索更加符合实际的模型,从而为保险公司提供理论上的依据.
本文结合目前的经济发展情况和保险业多险种的状况,考虑了常利率、通货膨胀率和利息力的影响分别建立了三个风险模型.
第一个模型是考虑的是常利率和常通货膨胀率对初始资金和每次收取保费的影响下,保费收取和索赔都服从possion分布的风险模型,并且运用鞅方法得到了最终破产概率.
第二个模型是在第一个模型的基础上,把单险种推广到双险种的研究,考虑索赔服从possion分布和负二项分布,得到了最终破产概率.
第三个是在前两个模型基础上,考虑到保费收取和索赔额都受利息力的影响的一个模型,这个模型更加符合实际的需要,进而运用鞅分析的方法得到了破产概率和lundberg上界.
In the market-oriented economy, all activities included insurance industry are being affected by interest rate. Except that, insurance is a risky activity, so Insurance Companies are concerned more about how to avoid risks and stable operation. As a result, scholars are increasingly exploring more realistic models, so as to provide a theoretical basis for the insurance company.
In this text ,I built three models based on the economic development and the status of multi-line insurance, and consider the constant interest rates and the inflation rate .
The first model is to consider the constant rate and constant rate of inflation, the premium and claims are confined to passion process, and the upper bound of the ruin probability by martingale approaches and the bound of lundberg were obtained.
The second model is based on the first model, considering the double-type-insurance. the claims are confined to passion process and negative binomial process. And the ruin probability are obtain.
The third model is based on the first two models, the claim and the premium are both impacted by the force of interest, then the upper bound of the ruin probability by martingale approaches was obtained.
本文结合目前的经济发展情况和保险业多险种的状况,考虑了常利率、通货膨胀率和利息力的影响分别建立了三个风险模型.
第一个模型是考虑的是常利率和常通货膨胀率对初始资金和每次收取保费的影响下,保费收取和索赔都服从possion分布的风险模型,并且运用鞅方法得到了最终破产概率.
第二个模型是在第一个模型的基础上,把单险种推广到双险种的研究,考虑索赔服从possion分布和负二项分布,得到了最终破产概率.
第三个是在前两个模型基础上,考虑到保费收取和索赔额都受利息力的影响的一个模型,这个模型更加符合实际的需要,进而运用鞅分析的方法得到了破产概率和lundberg上界.
In the market-oriented economy, all activities included insurance industry are being affected by interest rate. Except that, insurance is a risky activity, so Insurance Companies are concerned more about how to avoid risks and stable operation. As a result, scholars are increasingly exploring more realistic models, so as to provide a theoretical basis for the insurance company.
In this text ,I built three models based on the economic development and the status of multi-line insurance, and consider the constant interest rates and the inflation rate .
The first model is to consider the constant rate and constant rate of inflation, the premium and claims are confined to passion process, and the upper bound of the ruin probability by martingale approaches and the bound of lundberg were obtained.
The second model is based on the first model, considering the double-type-insurance. the claims are confined to passion process and negative binomial process. And the ruin probability are obtain.
The third model is based on the first two models, the claim and the premium are both impacted by the force of interest, then the upper bound of the ruin probability by martingale approaches was obtained.
引文
[1]孙立娟,顾岚.保险公司赔付及破产的随机模拟域分析[J].数理统计与管理,1999(2):25-30.
[2]邹辉,朱勇华.保险精算中的一个破产概率的改进[J].武汉水利电力大学学报,2000(2):33-35.
[3]方世祖,罗建华.双复合possion风险模型[J].纯粹数学与应用数学,2006(6):271-277.
[4] Grandell.J.Aspects of risk theory[M].New York:Springer-Verlag.1991.
[5]何树红,徐兴富.双Cox风险模型[J].云南大学学报自然科学版,2004(4):275-278.
[6]高珊.一类带干扰的Cox风险模型.贵州师范大学学报自然科学版,2005(3):63-66.
[7] Gerber H.U.,Goovaerts, M.J., Kass, R. On the probility and serverity of ruin[J]. ASTIN BULLETIN, 1987(17):151-163.
[8] Gerber H.U.着,成世学,严颖译.数学风险论导引[M].世界图书出版社, 1979.
[9] Dufresne, F.,Gerber H.U.,The surpluses immediately before and at ruin, and the amount of the claim causing ruin[J]. Insurance:Matics and Economics, 1988(7):193-199.
[10]蔡高玉,耿显名.带干扰的双复合possion风险模型[J],大学数学,2007(2):256-259.
[11] Gerber.H.U.Ruin theory in the linear model. Mathematics and Economics,1982:177-184.
[12]王文波,王慧丽.一类相依索赔离散风险模型研究.纯粹数学与应用数学,2008(2).
[13]唐启鹤.重尾索赔下关于破产概率的一个等价式.Science in China,2002(2).
[14]唐启鹤,严家安..A sharp inequality for the tail probabilities of sums of i.i.d. r.v.s with dominatedly varying tails. cience in China,2002(8).
[15]唐启鹤.An asymptotic relationship for ruin probabilities under heavy-tailed claims. cience in China,2002(5).
[16] Non-exponential bounds for ruin probability with interet Effect included,Scandinavian Actuarial Journal,1(1998),66-79.
[17]孙丽娟,顾岚.离散时间保险风险模型的破产概率问题.应用概率统计[J],2002(8):293-299.
[18]翁小勇,杨娟.随机利率及保费的离散风险模型中的破产概率.数学杂志[J],2009(3): 335-338.
[19]于莉.带有变利率的离散时间风险模型的概率分布.合肥工业大学学报[J],2009(2):273-277.
[20]赵霞.鞅方法在一类破产概率中的应用.经济数学[J],2002(2):15-20.
[21]陈世平.精算数学中的鞅方法.数学理论与应用[J],2003(3):12-16.
[22]董英华,张汉君.带干扰的双possion风险模型的破产概率[J].数学理论与应用,2003(3):98-101.
[23]韩丽,孔繁亮.一类推广后的双风险模型破产概率的鞅分析[J].数理统计与管理,2007(11):112-115.
[24]陈东.标准索赔额下带干扰的破产模型研究[J].湖南文理学院学报自然科学版,2007(4):39-41.
[25]聂高琴,刘次华.随机保费率下带干扰风险模型的破产概率[J].华中师范大学学报自然科学版,2005(9):301-303.
[26]郭立娟,刘冬元.一类广义双险种二项风险模型的破产概率[J].数学理论与应用2007(27)113-115.
[27]陈茜,余蓝萍,随机利率下的双险种风险模型[J].数学理论与应用, 2007(4):114-117.
[28]何树红,陈焱.常利率因素的双险种风险模型[J].云南大学学报自然科学版,2006(2):73-76.
[29]李静霞,王永茂.常利率因素下的双险种风险模型[J].数学理论与应用,2008(1):101-106.
[30]孙立娟,顾岚.离散时间模型下的最大赤字问题[J].经济数学,2001(12):1-9.
[31]何莉娜,刘再明.保费收取为随机过程且带利率的破产模型[J].吉首大学学报自然科学版,2006(3):9-11.
[32] JUN CAI, DAVID C.M.DICKSON. Ruin Probabilities With a Markov Chain Internet Model[J].Mathematical and Economiics,2001:217-229.
[33]樊平毅.随机过程理论与应用[M].清华大学出版社,2005.
[34]何莉娜,刘再明.钱敏平,龚光鲁.随机理论过程[M].北京大学出版社,1997.
[35]刘伟,吴黎军.带干扰的双负二项风险模型的破产概率[J].乌鲁木齐职业大学学报,2006(6):59-63.
[36]孙道德.负二项分布的性质及其应用[J].阜阳师范学院学报,2000(5):10-12.
[2]邹辉,朱勇华.保险精算中的一个破产概率的改进[J].武汉水利电力大学学报,2000(2):33-35.
[3]方世祖,罗建华.双复合possion风险模型[J].纯粹数学与应用数学,2006(6):271-277.
[4] Grandell.J.Aspects of risk theory[M].New York:Springer-Verlag.1991.
[5]何树红,徐兴富.双Cox风险模型[J].云南大学学报自然科学版,2004(4):275-278.
[6]高珊.一类带干扰的Cox风险模型.贵州师范大学学报自然科学版,2005(3):63-66.
[7] Gerber H.U.,Goovaerts, M.J., Kass, R. On the probility and serverity of ruin[J]. ASTIN BULLETIN, 1987(17):151-163.
[8] Gerber H.U.着,成世学,严颖译.数学风险论导引[M].世界图书出版社, 1979.
[9] Dufresne, F.,Gerber H.U.,The surpluses immediately before and at ruin, and the amount of the claim causing ruin[J]. Insurance:Matics and Economics, 1988(7):193-199.
[10]蔡高玉,耿显名.带干扰的双复合possion风险模型[J],大学数学,2007(2):256-259.
[11] Gerber.H.U.Ruin theory in the linear model. Mathematics and Economics,1982:177-184.
[12]王文波,王慧丽.一类相依索赔离散风险模型研究.纯粹数学与应用数学,2008(2).
[13]唐启鹤.重尾索赔下关于破产概率的一个等价式.Science in China,2002(2).
[14]唐启鹤,严家安..A sharp inequality for the tail probabilities of sums of i.i.d. r.v.s with dominatedly varying tails. cience in China,2002(8).
[15]唐启鹤.An asymptotic relationship for ruin probabilities under heavy-tailed claims. cience in China,2002(5).
[16] Non-exponential bounds for ruin probability with interet Effect included,Scandinavian Actuarial Journal,1(1998),66-79.
[17]孙丽娟,顾岚.离散时间保险风险模型的破产概率问题.应用概率统计[J],2002(8):293-299.
[18]翁小勇,杨娟.随机利率及保费的离散风险模型中的破产概率.数学杂志[J],2009(3): 335-338.
[19]于莉.带有变利率的离散时间风险模型的概率分布.合肥工业大学学报[J],2009(2):273-277.
[20]赵霞.鞅方法在一类破产概率中的应用.经济数学[J],2002(2):15-20.
[21]陈世平.精算数学中的鞅方法.数学理论与应用[J],2003(3):12-16.
[22]董英华,张汉君.带干扰的双possion风险模型的破产概率[J].数学理论与应用,2003(3):98-101.
[23]韩丽,孔繁亮.一类推广后的双风险模型破产概率的鞅分析[J].数理统计与管理,2007(11):112-115.
[24]陈东.标准索赔额下带干扰的破产模型研究[J].湖南文理学院学报自然科学版,2007(4):39-41.
[25]聂高琴,刘次华.随机保费率下带干扰风险模型的破产概率[J].华中师范大学学报自然科学版,2005(9):301-303.
[26]郭立娟,刘冬元.一类广义双险种二项风险模型的破产概率[J].数学理论与应用2007(27)113-115.
[27]陈茜,余蓝萍,随机利率下的双险种风险模型[J].数学理论与应用, 2007(4):114-117.
[28]何树红,陈焱.常利率因素的双险种风险模型[J].云南大学学报自然科学版,2006(2):73-76.
[29]李静霞,王永茂.常利率因素下的双险种风险模型[J].数学理论与应用,2008(1):101-106.
[30]孙立娟,顾岚.离散时间模型下的最大赤字问题[J].经济数学,2001(12):1-9.
[31]何莉娜,刘再明.保费收取为随机过程且带利率的破产模型[J].吉首大学学报自然科学版,2006(3):9-11.
[32] JUN CAI, DAVID C.M.DICKSON. Ruin Probabilities With a Markov Chain Internet Model[J].Mathematical and Economiics,2001:217-229.
[33]樊平毅.随机过程理论与应用[M].清华大学出版社,2005.
[34]何莉娜,刘再明.钱敏平,龚光鲁.随机理论过程[M].北京大学出版社,1997.
[35]刘伟,吴黎军.带干扰的双负二项风险模型的破产概率[J].乌鲁木齐职业大学学报,2006(6):59-63.
[36]孙道德.负二项分布的性质及其应用[J].阜阳师范学院学报,2000(5):10-12.