两个内部交易者混合策略均衡高频交易的渐近分析

发布时间：2018-02-01 08:58

本文关键词： 内部交易高频交易博弈论做市商混合策略渐近分析　出处：《长沙理工大学》2013年硕士论文　论文类型：学位论文

【摘要】：本文以Gong和Zhou(2010)模型为原型,对内部交易问题做了扩展研究。该模型中假设市场中存在一项风险资产,关于该风险资产参与交易的交易者分为三类：首先是内部交易者,拥有私有信息,以自身利润最大化为目标选择最优的交易策略,并假设内部交易者个数为2；其次为噪声交易者,没有任何的私有信息,客观上为内部交易者提供了掩护；第三类交易者为做市商,根据内部交易者和噪声交易者的提交交易量之和,结合公开的历史信息,制定理性预期价格。本文对均衡定义做了两条假设：1.内部交易者利润最大化：在每一期交易,内部交易者根据私有信息和历史信息以及对风险的态度选择最优交易量,以最大化相应预期未来总利润的相关部分；2.市场有效性条件：价格序列关于总交易量序列生成的信息流为鞅。本文研究了三个模型：1.两个内部交易者为风险喜好：先最大化风险利润,然后最大化保底利润；2.两个内部交易者为风险中性：最大化事前预期未来总利润；3.两个内部交易者为风险厌恶：首先最大化保底利润,然后最大化风险利润。在高频交易情况下,本文主要考虑了三类内部交易者混合策略均衡的渐近分析。这里高频交易是指：在[0,1]时间区间内,交易次数很多,每次交易间隔时间很短。当交易次数趋于无穷大时,直接对其中的经济金融变量序列取极限获得的结果是平凡的,即所获得的极限结果为零或无穷.因此,本文需要使用渐近分析的方法对高频交易情况下三类内部交易者的混合策略均衡进行了分析和讨论,不仅计算了经济金融变量序列趋于零或无穷的速度,而且获得了这些经济金融变量序列除以相应收敛速度后所得的规范化变量序列的极限,因此获取了相应的非平凡连续解。本文的主要结果为：交易强度、剩余信息量和市场流动性参数的变化速度以及它们规范化后的极限,并与Gong和Zhou(2010)模型中市场上仅有一个内部交易者的相应结果进行了比较分析,讨论了内部交易者个数和风险属性对于交易强度、剩余信息量和市场流动性参数的影响。
[Abstract]:This paper takes the Gong and Zhou 2010 models as the prototype and makes an extended study on the internal trading problem. The model assumes that there is a risky asset in the market. There are three types of traders involved in the trading of the risky assets: first, the internal traders have private information and choose the optimal trading strategy with the goal of maximizing their own profits, and assume that the number of internal traders is 2; Secondly, noise traders, without any private information, objectively provide cover for internal traders; The third type of traders are market makers. According to the sum of the transaction volume submitted by internal traders and noise traders, rational expected prices are formulated in combination with public historical information. This paper makes two assumptions on the definition of equilibrium: 1. The profit maximization of internal traders: in each transaction, internal traders choose the optimal trading volume according to private information and historical information, as well as the attitude towards risk. To maximize the relevant portion of the corresponding expected future total profit; 2. Market efficiency condition: the information flow generated by the price sequence on the total trading volume sequence is martingale. This paper studies three models: 1. Two internal traders are risk preference: first to maximize risk profit, then to maximize guaranteed profit; 2. The two internal traders are risk-neutral: to maximize the expected future total profit; 3. Two internal traders are risk-averse: first maximize guaranteed profits, and then maximize risk profits. In the case of high frequency trading, this paper mainly considers the asymptotic analysis of mixed strategy equilibrium of three kinds of internal traders. [In the time range, the number of transactions is many, and the time between each transaction is very short. When the number of transactions tends to infinity, the result obtained by taking the limit of the economic and financial variables directly is ordinary. Therefore, we need to use asymptotic analysis method to analyze and discuss the mixed strategy equilibrium of three kinds of internal traders in the case of high frequency trading. Not only the speed of the sequence of economic and financial variables approaching zero or infinity is calculated, but also the limit of the sequence of normalized variables obtained by dividing the sequence of economic and financial variables by the corresponding convergence rate is obtained. Therefore, the corresponding nontrivial continuous solutions are obtained. The main results of this paper are as follows: the trading intensity, the amount of residual information and the changing speed of the market liquidity parameters and their standardized limits. And compared with the corresponding results of only one internal trader in the market in Gong and Zhou 2010) model, and discussed the number of internal traders and risk attributes for the trading intensity. The effect of residual information and market liquidity parameters.
【学位授予单位】：长沙理工大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F830.91;F224

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