证券价格波动模型的动力学研究

项目名称： 证券价格波动模型的动力学研究

项目编号： No.10871005

项目类型： 面上项目

立项/批准年度： 2009

项目学科： 金属学与金属工艺

项目作者： 王铎

作者单位： 北京大学

项目金额： 24万元

中文摘要： 金融动力学近年来发展非常迅速。它着眼于从市场内部具有不同理念投资者的交易行为和市场交易规则中发现引起金融价格复杂波动的原因，取得许多重要成果。金融动力学已经成为金融学举足轻重的重要研究领域。我们取得如下一些重要进展：1）部分地解决了金融动力学研究的一个重要的疑难问题。原来金融动力学研究总是把有随机外生变量的动力学模型简化为确定性动力学模型，然后把确定性动力学模型的研究结果用于对金融的解释。但这样做的合理性并未得到证明。我们首先得到了随机差分方程平稳解的存在性稳定性和收敛性的新结果，进而论证了上述研究方法在一定条件下是合理的；2）首次提出带库存的做市商定价模型，并发现了做市商并不能保证金融价格的稳定性；3）直接研究具有随机因素的互异代理人的金融动力学模型，并通过平稳分布研究市场的均衡价格，为金融动力学研究提供新的研究思路；4）对市场上真实投资者普遍的对信息的不对称反应引入金融动力学模型，发现这种不对称反应也是价格波动的重要原因；5）对具有时滞的金融动力学模型的研究发现了时滞对金融价格的复杂影响；6）利用临界点理论研究时滞微分方程得到多周期解的存在性，为研究时滞金融动力学模型提供了新方法。

中文关键词： 金融动力学;随机动力系统;证券价格波动;做市商;时滞

英文摘要： The studies of financial dynamical systems developed very fast recently. The aim is to find reasons of fluctuation of financial prices from the trading behaiviors and trading rules of financial markets, and have achieved many important results. So financial dynmaical study is already one of important fields in finance. We have got the following results:1) We partly solved an important problem in the fields of financial dynamic. For financial dynamical models, most of them are including some random external variables, they are always to be implified as deterministic dynamical models first and then the properties of the deterministc models are used to explain the financial markets. But the resonableness of this method has never been proved. We first got a new result for random difference equations, proved the existence,stability and convergence of stable solutions and then applied to financial dyanmical model with random dividend. We showed that the deterministic dynamical model is indeed good approximation for the original random model; 2) We first introduced a dynamical model with inventory for market maker trading system and found that market makers may not stabilize the market; 3)We studied directly the stochastical financial models with heterogeneous agents, used the stationary measure to study equilrium price, introduced a new idea for financial dyanmical study; 4)We introduced the asymmetric reaction to financial trading information in financial dynamcial models and found that the asymmetry is also an important reason for fluctuation of asset prices; 5)We studied the financial models with time delay and found that the time delay may influnce the price in a very complex way; 6)We applied the variation method and Morse theory to study the existence of periodic solutions of delay differential equations and got some new results which may be used to financial studies.

英文关键词： financial dynamics; random dynamical system; fluctuation of asset price; market maker;time delay