文档介绍：摘要
摘要
随着股票市场的发展,市场参与者数量日益庞大,竞争激烈,在某种程度上,市场已经初步达到了弱有效市场假设的理论定义。本文主要介绍了有效市场理论,并在弱有效市场假设成立的前提下,讨论个人股票投资的最优策略问题。
由于金融市场的不确定本质,从一般经济均衡的角度出发对金融资产定价是不适宜的,最终改为由无套利假设理论出发,对金融资产进行定价。有效市场的问题最初讨论就是市场是否符合无套利假设。而对市场弱有效形式的检验通常归结为对市场鞅性质的检验。
在市场弱有效形式成立的前提下,股票价格过程具有马尔科夫性,可用动态规划的方法解决股票投资的最优策略问题。具体方法是在离散状态下,采用贝尔曼方程的逆序递推形式,在理论上解决股票最优投资的全买全卖策略问题, 并与经典的技术分析理论作比较;在连续状态下,无风险资产(政府债券)和股票价格过程遵循几何布朗运动,根据最优性原理,引入随机最优控制中的值函数,运用HJB方程求解最优投资策略,使投资人的期望效用最大化。
离散状态下,可以得出通常所说的“最低点买入,最高点卖出"的结论, 收益率由后期的股价来表示,但是后期股票价格未知,需要另外讨论。连续状态下,选取特定的效用函数,可以得到股票投资的最优策略的解析解。后续工作中,可以在股票的价格模型中加入跳扩散过程,跳扩散过程可用修改的泊松累计过程来表示,还可以加入交易费用,红利分红等实际信息,但是由于值函数是二阶微分方程形式,所以求出解析解还是比较困难,可考虑求数值解。关键词:有效市场理论:动态规划;几何布朗运动;随机最优控制
Abstract
With the development of stock market,there exists跹increasingly large number of market participants and some extent,the market has preliminarily conformed to the theoretical definition of the weak efficient market
this paper,I mainly illuminate the efficient market theory,and discuss the optimal individual stock investment strategy based on the weak efficient market
hypothesis.
It is not appropriate to price the financial assets from the perspective of general economic equilibrium replaced by the theory of no·arbitrage hypothesis ultimately, because of the nature of uncertainty in the financial initial discussion about the efficient market is whether market is according with no—arbitrage usually,the test for the weak efficient market boils down to the test
of the martingale properties of markets.
Under the premise of the establishment of the weak efficient market,the stock price process has the Markov call solve the optimal stock investment strategy problem using the reverse recursive equation of the dynamic programming method in the discrete the continuous state,risk—free assets(government bonds)and stock price process follows geometric Brownian to the optimum principle,we introduced the value function of the