【作者】 孙倩；

【导师】 林正炎；

【作者基本信息】 浙江大学 ， 概率统计， 2009， 硕士

【摘要】 经典的破产概率模型奠定了破产理论的研究基础。然而,随着经济金融形势的日趋复杂,保险公司业务的推广,经典模型中的假设已经无法满足对保险公司破产概率评估的需要。为了保证保险公司更为稳健地经营,针对不同险种分别研究,或者对多险种综合考虑来评估保险公司的经营状况非常必要。已经有大量文献对经典模型进行了多方面的推广和扩展,但大部分文章假定保险公司只经营一类险种,或者假定所有经营险种的各期总索赔满足一定规律的分布,即可以将所有险种的总索赔看作一个随机变量。这种假定简单易行,但不容易了解保险公司各险种之间的相互影响以及哪个险种是导致保险公司破产的主要原因。本文主要从多险种的角度入手对模型进行推广,并对其破产概率进行了研究,主要内容如下。第一章,介绍了破产理论和方法、研究成果及本文的主要内容和结构。第二章,建立双险种一维离散风险模型,求解其破产概率在索赔为重尾分布时的近似分布,并利用归纳法给出其小额索赔时相应的破产概率上界。第三章,建立多险种的离散多维风险模型,并用鞅方法求解其在一定条件下的破产概率上界。本文的创新之处在于从多险种角度考虑问题,建立新的风险模型。一种是一维风险模型,索赔可能服从多种分布,且各期索赔是相关的,这里用Marcov链来表达这种相关性,而不是用连接函数。另一种是引入高维的风险模型,对各险种分别建立盈余过程,用AR（p）描述索赔量之间的相关性,并定义破产时间T_max=min{n≥0|U（n）＜0},从而评估破产概率的上界。更多还原

【Abstract】 The classical ruin model builds the basic knowledge of ruin theory. However, when the international financial circumstances become more and more complex, and when the insurance companies make more efforts to occupy a wider market, the assumptions in the classical model are far from being desired. So it is totally necessary to take multi-insurance codes into consideration to guarantee a more stable operation.The classical risk model has been generalized to a new one by many people until now. Well, most of the generalizations assume that there is only one kind of claim distribution. It is easy to calculate, while the results cannot show the differences among different insurance codes and the effect that every kind of insurance makes to the final ruin probability. In this paper, the model is generalized in the way that multi-insurance codes are considered. The main content is as follows:Chapter I, we introduce the basic ruin theory and methods, the main conclusions, and the structure of this paper.Chapter II, we build a one-dimensional risk model containing two kinds of claim possibilities. Then we get the approximation of the ruin probability when the beginning surplus is large enough. Also, we can analyze the upper bound of the ruin probability when the claim size is not very large.Chapter III, we build a multi-dimensional risk model for multi-insurance codes, and use martingale method to get the upper bound of the ruin probability.The creative point in this paper is that we build the model from the multi-insurance codes point of view. One is one-dimensional with claims correlated with each other and having more than one kind of distributions. Here, we use Marcov Chain instead of copula to model the correlation between claims. The other is a multi-dimensional risk model, which builds surplus process for every insurance code, uses AR（p） to describe the correlation between claims, and defines ruin time as T_max = mm{n≥0| U（n） < 0} to evaluate the upper bound of ruin probability.更多还原