随机市场深度下多资产的最优执行问题  

The optimal portfolio execution problem with the stochastic market depth

作　　者：冯玲 林雨 吴伟平 王曈瑶 FENG Ling;LIN Yu;WU Weiping;WANG Tongyao(School of Economics and Management,Fuzhou University,Fuzhou 350108,China;Department of Automation,Shanghai Jiao Tong University,Shanghai 200240,China)

机构地区：[1]福州大学经济与管理学院,福州350108 [2]上海交通大学自动化系,上海200240

出　　处：《系统工程理论与实践》2022年第7期1811-1825,共15页Systems Engineering-Theory & Practice

基　　金：国家自然科学基金(71573043,71973028)。

摘　　要：投资者对金融资产的供求往往随着市场波动而不断变化,并随时进行下达和取消订单等交易行为,故而市场的流动性在本质上是随机波动的.因此,本文研究了当市场深度随机变化时,限价指令簿市场中多资产的最优执行问题,并采用动态规划的方法给出了最优执行策略及最小执行成本的解析表达式.结果表明,最优执行策略是关于位移和剩余头寸的线性函数,而最优执行成本则是关于初始资产购买量的非线性函数.数值算例显示,当投资者忽略市场深度的随机波动特征及资产价格的相互交叉影响时,将会导致支付较大的交易成本,从而降低投资的福利水平.The supply and demand of financial assets for investors,who can place and cancel limit orders at any time,often changes continuously with market fluctuations.And it causes the randomness of market liquidity.This paper studies the optimal portfolio execution problem with the stochastic market depth in the limit order book(LOB)market.We develop successfully the analytical optimal execution strategy and minimum execution cost for such a problem by using the dynamic programming method.The revealed results show that the obtained optimal execution strategy is a linear function with respect to the displacement and remaining position.Moreover,the optimal execution cost is a non-linear function of the initial asset quantity.The numerical examples show that the investor would pay higher transaction costs and reduce the level of investment welfare when they ignore the random fluctuation characteristics of market depth and the cross-effect between asset prices.

关 键 词：随机流动性 限价指令簿 最优执行问题 价格相关影响 动态规划 

分 类 号：F830.9[经济管理—金融学]