经典风险过程和对偶模型中的投资问题

发布时间：2018-04-22 10:20

本文选题：随机控制 + H-J-B方程　；参考：《中南大学》2013年硕士论文

【摘要】：近年来,保险公司及其他一些行业,由于竞争的加剧,他们需要更好的管理市场和经营风险,保险者经常通过一些商业举措,比如投资(investment)和再保险(reinsurance),来尽量控制他们的风险。特别是当保险公司在处理很大数额的赔付情形之下,经常需要对赔付进行再保险处理,并考虑再保险的策略问题。因此在保险的风险管理领域内,衍生了许多关于多个目标或多维目标的最优化问题。而对这些问题的研究和学习是很益于企业的管理和发展的。在本文中,我们首先对保险公司的情形进行分析,我们讨论了当一个保险公司的资产满足经典风险盈余过程时试图最大化最终财富的期望效用问题,这个最优化问题同时考虑其在金融市场的投资和自身的超额损失再保险(excess-of-loss reinsurance)两种行为策略。在下一部分,我们研究了一些其他的行业,它们具有这样的一种特点,做持续的支出而获得偶然的收益。对于这种对偶模型(dual model),我们也讨论了它的最优投资策略问题。本文在描述金融市场风险资产的模型时,我们放弃了经典的Black-Scholes几何布朗运动模型而采取了更加符合实际的Oristein-Uhlenbeck模型,这使得股票价格过程呈现出牛市和熊市的特征,更加准确的贴合了现实世界。我们通过随机控制理论和求解相应的Hamilton-Jacobi-Bellman(HJB)方程,得到我们的最优的再保险-投资策略和相应值函数的显示形式解,给保险公司和一些其他行业在相关风险管理和投资领域的行为提供一些良好的建议。
[Abstract]:In recent years, insurance companies and other industries have needed better management of market and operating risks as a result of increased competition, and insurers often try to control their risks through business initiatives such as investment investment and reinforcements. Especially when the insurance company is dealing with a large amount of compensation, it is often necessary to reinsurance the compensation, and consider the reinsurance strategy. Therefore, in the field of risk management of insurance, there are many optimization problems about multiple objectives or multidimensional objectives. The research and study of these problems is beneficial to the management and development of enterprises. In this paper, we first analyze the situation of insurance companies. We discuss the expected utility of maximizing the ultimate wealth when an insurance company's assets satisfy the classical risk surplus process. This optimization problem considers both its investment in financial markets and its own excess loss reinsurance strategy. In the next section, we look at other industries that have the trait of making occasional gains from sustained spending. For this dual model, we also discuss its optimal investment strategy. In this paper, we abandon the classical Black-Scholes geometric Brownian motion model and adopt a more realistic Oristein-Uhlenbeck model, which makes the stock price process show the characteristics of bull market and bear market. A more accurate fit for the real world. By using stochastic control theory and solving the corresponding Hamilton-Jacobi-Bellmanian HJB equation, we obtain our optimal reinsurance and investment strategy and the display form of the corresponding value function. Provide some good advice to insurance companies and other industries in related risk management and investment areas.
【学位授予单位】：中南大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F830.91;F224

【共引文献】