【作者】 陈丽；

【导师】 何传江；

【作者基本信息】 重庆大学 ， 应用数学， 2012， 硕士

【摘要】 在这个经济高速发展的时代，人们生活中所面临的各种不确定性和风险逐渐增加，使得风险理论的研究也在逐渐深入，其中破产概率成为风险理论中越来越受关注的研究内容。并且随着国际形势的动荡，越来越多的因素被引进了破产概率的研究中，比如日益增加的巨额保单使得再保险成为非常重要的一个环节，国际金融市场的不稳定，也使学者们意识到利率的重要性。经典风险模型是对破产概率研究中应用得最为广泛的模型，本文从实际需要出发，对经典风险模型进行改进，引进对模型有影响的一些因素，得出了关于破产概率的一些结论。本学位论文所做的主要研究结果如下：1.考虑了现实社会中大额保单的增多，以及越来越多的巨额风险的不断增加，在经典模型中加入再保险，使得改进后的模型更加符合保险公司的现状，而且更有利于维护保险公司的稳定；同时，考虑市场因素的影响，在模型中引入利率，对模型进行进一步的推广，建立了带常数利率的再保险风险模型。2.对建立的再保险模型进行研究，从保险公司盈余入手，分别就连续和离散两种情形进行讨论。其中，针对连续型模型利用微分方程的方法进行推导，得到了破产概率的积分表达式，并给出了当索赔额服从指数分布，且再保险形式为成数再保险时，破产概率的具体表达式，该表达式与经典风险模型的结论是一致的；针对离散型的模型，采用的是递推的方法，并应用归纳法证明所需结论，得到了破产概率的隐式表达式以及破产上界。更多还原

【Abstract】 With the rapid development of the economic，the uncertainties and risks that peopleare facing in the daily life are increasing gradually, so do the researches of the risktheory, especially, the ruin probability is becoming one of the most important parts ofthe studies. Moreover, because of the turbulence of the international situation, more andmore factors are taking into the studies of the ruin probability, for example, theincreasing huge insurance policies make the reinsurance to be an important aspect; theresearchers realize the importance of the interest rates because of the instability ofinternational financial markets.The classical risk model is one of the most important models in the industry of theruin probability. We modify it with some kinds of methods according to the reality’sdemand. At the same time, considering the impacts of the constant interest rates and thereinsurance, we get some conclusions about ruin probability.The main results of this paper are summarized as follows：1. Considering the increasing huge insurance policies and uncertain risks in the reallife, we improve the classical risk model to meet the present situation of the insurancecompany, and it is more effective to maintain the stability of the insurance companybecause of the improved model. In addition, we discuss the impacts of the marketfactors and add the interest rate in the reinsurance risk model to make it to be furtherpromoted. Since then, we get the reinsurance risk model with the impact of the constantinterest rate.2. Starting from the surplus process, we discuss continues and discrete casesrespectively of the model above. For continues reinsurance risk model, the integralexpression of the ruin probability and its upper bound are obtained by using themethods of differential equations and recursive calculations; besides, we get the exactexpression of the ruin probability when the individual claim has an exponentialdistribution with quota reinsurance, and the expressions are similar to the conclusions ofthe classical risk models. But for the discrete reinsurance risk model, we use the way ofrecursive calculations to get the expression and the upper bound of the ruin probability,and we prove the conclusions by using the method of the induction.更多还原