最优投资消费模型及其数值方法的研究

发布时间：2018-01-08 23:29

本文关键词：最优投资消费模型及其数值方法的研究　出处：《中国石油大学》2009年硕士论文　论文类型：学位论文

【摘要】： 最优投资消费问题由来已久,每个人、每个经济实体几乎每天都面临着一个投资消费决策问题。面对现实生活中大量的不确定性因素,特别是近年来重大金融突发事件的发生以及金融变革中的诸多问题,人们发现经典Merton模型已不能完全适应现代金融市场的变化。本文在考虑现实生活中存在各种影响投资和消费活动的因素的情形下,采用随机最优控制理论和对偶理论,分别研究了以下几种连续时间框架下投资组合与消费问题并对最优策略进行了求解,进而揭示其在现实应用中的意义。本文的主要研究工作和所得结果集中在第三到第五章。第三章中假设投资者的死亡事件是随机的,研究了贷款利率大于存款利率时投资者具有随机收入的最优投资消费问题。首先建立了问题的随机最优控制模型,运用动态规划方法和对偶理论,得到了相应的HJB方程,进而得到一般情形下具有反馈形式的最优消费与投资策略;其次,讨论了效用函数为一类特殊的HARA情形时最优策略的具体形式;最后,与经典的Merton问题进行了比较分析。第四章研究了具有异常波动的金融市场中的最优投资消费问题,考虑投资者的消费对象同时包括可存品与非可存品的情况。首先给出了最优投资消费问题的随机最优控制模型,然后运用动态规划方法,对于幂效用函数情形,得到了最优策略显式解,最后对最优解进行了分析说明。第五章主要围绕具有成比例交易费用的最优投资消费问题的数值解进行讨论,首先给出该问题的数学模型及其控制方程(HJB方程),一般该HJB方程很难求得显示解,本章在H.Liu(2004)文献的基础上,根据已有的结论,提出了一种求解具有交易费用的最优投资消费模型的数值算法,并通过数值例子验证了算法的可行性,其所求得的无交易区域与原算法吻合。
[Abstract]:Long-standing, optimal investment and consumption each person, each economic entity almost every day facing a consumption and investment decision problem. To face the reality of life in a lot of uncertain factors, especially many problems in recent years, major financial events and financial reform, people find that the classic Merton model has not fully adapt to the change of modern in the financial market. Considering the existence of factors of the investment and consumption activities of the various effects of real life, using stochastic optimal control theory and duality theory, respectively study the following continuous time under the framework of investment portfolio and consumption problem and the optimal strategy for solving, and to explore its application in the real sense.
The main research work and the results to the fifth chapter in third. Assuming the investor's death event in the third chapter is random, the optimal investment and consumption of loan investors with a stochastic income. First, the stochastic optimal control model of the problem is established by using the dynamic programming method and duality theory, get the corresponding HJB equation, then get the optimal consumption and investment strategy with feedback in the form of general situation; secondly, discuss the utility function for a special HARA case when specific forms of the optimal strategy; finally, compared with the classical Merton problem. The fourth chapter studies the optimal investment and consumption with abnormal fluctuations in financial market, investors consider the consumption object including perishable goods and non durable goods. Firstly, the optimal investment consumption. Stochastic optimal control model of problem, and then using the dynamic programming method for the power utility function, the optimal strategy of explicit solution, the final solution is analyzed. The fifth chapter focuses on the optimal numerical optimal investment with transaction costs of the solution are discussed. Firstly, the mathematical model and control equation the problem (HJB equation), the general HJB equation is very difficult to obtain explicit solutions, this chapter in the H.Liu (2004) on the basis of the literature, according to the conclusion, put forward the numerical algorithm for solving the optimal investment consumption model with transaction costs, the feasibility of the algorithm is verified by a numerical example, the calculated the free trading area and the original algorithm is consistent.

【学位授予单位】：中国石油大学
【学位级别】：硕士
【学位授予年份】：2009
【分类号】：F224;F830.59;F014.5

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