常利率下带干扰的离散风险模型的研究
发布时间：2018-09-10 09:46
【摘要】：经典风险理论主要用来处理保险事务中的风险模型，其中研究最为彻底的要数经典风险模型。经典风险模型描述的是一种单险种且忽略众多因素的完美的风险模型，正因如此，它根本无法满足当今保险公司的实际需求，因而对多险种风险模型这样符合实际经营的模型研究就成为了必要。基于这种想法，本文讨论了双险种风险模型情形下的破产问题，并加入了常利率和干扰因子。在第三章中，就理赔到达分别服从Poisson过程和二项过程的离散型风险模型进行讨论，得到了此模型的最终破产概率及Lundberg不等式，并同时考虑了投资利率和通货膨胀的影响。本文还将保单到达过程推广，在第四章中建立了广义双二项风险模型，讨论盈余过程的性质，得到生存概率，，破产概率的一般表达式及Lundberg不等式。由于风险的不确定性，保险公司可以通过购买再保险来减少承保的风险，本文在第五章中介绍了比例再保险模型，利用鞅方法得到了破产概率，并利用拉格朗日乘数法求出收益最大化的最优自留比例。这样既加强了模型的现实描述能力，又对保险公司的安全经营及监督管理有重大意义。
[Abstract]:The classical risk theory is mainly used to deal with the risk model in insurance affairs, and the most thorough research is the classical risk model. The classical risk model describes a perfect risk model with a single type of insurance and neglects many factors. Because of this, it simply can not meet the actual needs of insurance companies today. Therefore, it is necessary to study the multi-insurance risk model which is in line with the actual operation. Based on this idea, the ruin problem in the case of double insurance risk model is discussed, and the constant interest rate and disturbance factor are added. In the third chapter, the discrete risk model of claim arrival from Poisson process and binomial process is discussed, the final ruin probability and Lundberg inequality are obtained, and the effects of investment interest rate and inflation are considered at the same time. In chapter 4, the generalized binomial risk model is established, and the properties of the surplus process are discussed. The general expressions of survival probability, ruin probability and Lundberg inequality are obtained. Because of the uncertainty of risk, insurance companies can reduce the risk of underwriting by buying reinsurance. In chapter 5, the proportional reinsurance model is introduced, and the ruin probability is obtained by using martingale method. The Lagrange multiplier method is used to calculate the optimal retention ratio. This not only strengthens the realistic description ability of the model, but also has great significance to the safety management and supervision and management of the insurance company.
【学位授予单位】：渤海大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F224;F840.3
本文编号：2234091
[Abstract]:The classical risk theory is mainly used to deal with the risk model in insurance affairs, and the most thorough research is the classical risk model. The classical risk model describes a perfect risk model with a single type of insurance and neglects many factors. Because of this, it simply can not meet the actual needs of insurance companies today. Therefore, it is necessary to study the multi-insurance risk model which is in line with the actual operation. Based on this idea, the ruin problem in the case of double insurance risk model is discussed, and the constant interest rate and disturbance factor are added. In the third chapter, the discrete risk model of claim arrival from Poisson process and binomial process is discussed, the final ruin probability and Lundberg inequality are obtained, and the effects of investment interest rate and inflation are considered at the same time. In chapter 4, the generalized binomial risk model is established, and the properties of the surplus process are discussed. The general expressions of survival probability, ruin probability and Lundberg inequality are obtained. Because of the uncertainty of risk, insurance companies can reduce the risk of underwriting by buying reinsurance. In chapter 5, the proportional reinsurance model is introduced, and the ruin probability is obtained by using martingale method. The Lagrange multiplier method is used to calculate the optimal retention ratio. This not only strengthens the realistic description ability of the model, but also has great significance to the safety management and supervision and management of the insurance company.
【学位授予单位】：渤海大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F224;F840.3
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