基于超额损失再保险的最优投资策略

发布时间：2018-01-31 06:42

本文关键词： 超额损失再保险 HJB方程投资破产概率扩散逼近　出处：《兰州理工大学》2014年硕士论文　论文类型：学位论文

【摘要】：最优投资与再保险是近年来金融学研究的热点问题之一,由于保险行业竞争激烈,为了增强企业竞争力,一方面,保险公司需要在金融市场上进行投资来获得收益,以提高公司的偿付能力和公司效益,而投资是保险公司获得资金的主要渠道之一；另一方面,为了减少大赔付的风险,保险公司需要分出部分保费来购买再保险,再保险可以使风险在各保险公司之间进行进行分摊,不仅可以提高保险经营的效率,同时,也促进了保险业经营的稳定性,实现了保险企业之间的利益共享和风险共担.因此,研究最优投资与再保险的策略问题,对保险公司具有很重要的理论基础和现实意义. 本文是利用随机控制理论的方法,通过建立数学模型研究了最优再保险与投资策略,以及如何提高自身的盈余水平和赔付能力使得保险公司破产概率最小的最优控制问题.首先,在带漂移系数的风险模型下,保险公司购买超额损失再保险,并将部分盈余投资于一些风险资产和无风险资产；其次,用扩散逼近的原理使离散的赔付过程连续化,得出了相应HJB方程的显式解,并证明了相关解的存在性与唯一性,并总结出在不同自留额下的最小破产概率、最优超额损失再保险和最优投资策略；最后,用MATLAB软件通过数值模拟计算分析了一些重要参数对最优超额损失再保险策略、最优投资策略和最小破产概率的影响,验证和得出了一些重要的结论.
[Abstract]:Optimal investment and reinsurance is one of the hot issues in finance research in recent years. Because of the fierce competition in the insurance industry, in order to enhance the competitiveness of enterprises, on the one hand. Insurance companies need to invest in the financial market to obtain income in order to improve the solvency and efficiency of the company, and investment is one of the main channels for insurance companies to obtain funds. On the other hand, in order to reduce the risk of large claims, insurance companies need to allocate part of the premium to buy reinsurance, reinsurance can make the risk between the insurance companies to share. It can not only improve the efficiency of insurance management, but also promote the stability of insurance business, realize the benefit sharing and risk sharing among insurance companies. It has important theoretical basis and practical significance for insurance companies. In this paper, the optimal reinsurance and investment strategy are studied by means of stochastic control theory and mathematical model. And how to improve their earnings level and the ability to pay the insurance companies to make the minimum probability of bankruptcy optimal control problem. Firstly, under the risk model with drift coefficient, insurance companies buy excess loss reinsurance. Part of the surplus is invested in some risky assets and risk-free assets; Secondly, the discrete compensation process is continuous by the principle of diffusion approximation, the explicit solution of the corresponding HJB equation is obtained, and the existence and uniqueness of the correlation solution are proved. The minimum ruin probability, the optimal excess loss reinsurance and the optimal investment strategy are summarized. Finally, the effects of some important parameters on the optimal excess loss reinsurance strategy, optimal investment strategy and minimum ruin probability are analyzed by numerical simulation with MATLAB software. Some important conclusions are obtained.
【学位授予单位】：兰州理工大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F840;F224

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