信用风险模型的破产问题

【作者】 刘东海；

【导师】 刘再明；

【作者基本信息】 中南大学 ， 概率论与数理统计， 2006， 硕士

【摘要】 经典风险模型及其推广为描述保险公司的经营状况提供了数学模型。考虑到保险公司的破产概率与信用风险有着密切的联系，同时考虑到资金的时间价值，本文对利率下的离散时间信用风险模型进行了研究。在第二章中，首先引入有限离散时间的一般信用风险模型及其相关结论。在第三章中，讨论了常利率下的信用风险模型，用递推的方法得到了有限时间内的破产概率和破产时间分布，并通过对破产概率的分析，得出了破产前盈余分布，破产时余额分布以及破产前、破产时余额的联合分布。在第四章中，在利率{r_n，n≥1}为独立同分布的情形下，进一步研究了利率下的离散时间信用风险模型，同样地得到了破产概率，破产时间分布，破产前盈余分布，破产时余额分布以及破产前、破产时余额的联合分布。特别地，当利率{r_n，n≥1)为常值序列时，即为常利率的信用风险模型，此时可以得到与第三章一样的结果。在第五章中，讨论了利率相依的离散时间的信用风险模型，得到了有限时间内破产概率和破产时间分布的递推公式，进而得出破产前盈余分布，破产时余额分布以及破产前、破产时余额的联合分布等结果。在第六章中对所得结果进行了分析，得到了一些有用结论。更多还原

【Abstract】 The classical and extensive risk models offer us mathematical modelsfor dealing with insurance company’s problems. Considering therelationship between the ruin probability and credit risk, also the fund’stime value included, the author discusses the finite discrete time insurancerisk model with credit risk under the interest force.In chapter 2, the author introduces the finite discrete time insurancerisk model with credit risk and some correlated results.In chapter 3, the author discusses the credit risk model under theconstant interest force. By using the recursive method, finite time ruinprobability and distribution of ruin time are obtained. Moreover, By theanalysis of ruin probability, the recursive formula for the distributions ofthe surplus before and at ruin, together with the joint distribution ofsurpluses are also derived.In chapter 4, When the interest force is independent identicallydistributed, the author discusses the discrete time insurance risk modelwith credit risk under the interest force, the recursive formula for thefinite time ruin probability, the distribution of ruin time, the distributionsof the surplus before and at ruin, together with the joint distribution ofsurpluses are also derived.In chapter 5, the author discusses the discrete time credit risk modelwith dependent rates. The recursive formula for the finite time ruin probability, the distribution of rain time, the distributions of the surplusbefore and at ruin, together with the joint distribution of surpluses arealso derived.In chapter 6, the author analyzes all the results and proposes theeffective conclusions.更多还原