CEV过程下含期权的最优投资问题研究

发布时间：2017-12-31 07:04

本文关键词：CEV过程下含期权的最优投资问题研究　出处：《上海师范大学》2014年硕士论文　论文类型：学位论文

更多相关文章： CEV过程 期权 套期保值策略 最优策略

【摘要】：随着金融市场的不断发展与完善,很多金融衍生产品,例如：期货,期权等等,已经成为市场上越来越多人的交易对象,因此,当投资对象中含有期权时如何安排自己的投资和消费是当前投资者所面临的实际问题。本文在CEV的过程下就投资对象中含有期权时的的一些问题进行了研究,并站在两种角度,结合实际情况进行分析,一种是站在个人投资角度进行考虑,另一种是站在企业,本文选取的是保险公司的角度进行分析。本文在第一章中介绍了投资消费问题和CEV的发展过程,第二章中介绍了本文模型所要用到的基本预备知识。第三章中考虑了含有无风险证券,风险证券以及以该风险证券为标的资产的欧式看涨期权的投资组合的最优投资以及消费问题,建立效用最大化模型,应用动态规划原理得到了关于指数效用函数下的最优投资消费策略,另外还得到了投资者的套期保值策略,并对这两种策略进行了比较,得到了它们之间的关系式。接着,在上文的基础上,继续考虑了当投资组合中含有多个风险证券时的情况,以及进一步考虑了当投资时间不确定时的最优投资消费问题。第四章中我们站在保险公司的角度上,研究了保险公司在随机保费下索赔额服从复合泊松过程的风险模型,通过投资市场上的风险证券以及以该风险证券为标的资产的期权,引用了财富效用函数,建立了最优投资问题.并根据随机控制理论得到了最大化财富的HJB方程,通过求解模型,得到了公司风险资产的配置额,最后对风险资产的投资进行数值模拟. 在第五章的结论与展望中,给出了本论文还存在的不足和今后要深入研究的方向。
[Abstract]:With the continuous development and improvement of financial market , many financial derivatives , such as futures , options and so on , have become more and more people in the market . Therefore , how to arrange their own investment and consumption is the actual problem faced by the current investors when the investment object contains the options . In the CEV process , we analyze some of the problems in the investment object , one is the point of view of the individual investment , and the other is the enterprise . In this article , the angle of the insurance company is analyzed . In chapter 1 , the paper introduces the development process of investment consumption and CEV , and introduces the basic preliminary knowledge to be used in the second chapter . In the third chapter , we consider the optimal investment and consumption problem of the portfolio of Europe - style call options which contain riskless securities , risk securities and the assets which are the subject assets of the risk securities , and establish the utility maximization model . The optimal investment consumption strategy under the function of the index is obtained by using the dynamic programming principle , and the relation between them is obtained . Then , on the basis of the above , the situation of the investment portfolio with multiple risk securities is considered , and the optimal investment consumption problem when the investment time is uncertain is further considered . In the fourth chapter , we have studied the risk model of the insurance company ' s claim to the compound Poisson process under the stochastic premium . Based on the risk securities on the investment market and the option of taking the risk securities as the target asset , this paper quotes the wealth utility function and establishes the optimal investment problem . According to the stochastic control theory , the HJB equation of maximum wealth is obtained . By solving the model , the allocation amount of the company ' s risk assets is obtained . Finally , the investment of the risk assets is simulated numerically . In the conclusion and prospect of the fifth chapter , the deficiency of this paper and the direction to be further studied in the future are given .

【学位授予单位】：上海师范大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F224;F830.91;F840.31

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