Optimal portfolio execution with a Markov chain approximation approach

IF 1.9 3区工程技术 Q3 MANAGEMENT

IMA Journal of Management Mathematics Pub Date : 2021-08-16 DOI:10.1093/imaman/dpab025

Jingnan Chen, Liming Feng, Jiming Peng, Yu Zhang

引用次数: 2

Abstract

We study the problem of executing a large multi-asset portfolio in a short time period where the objective is to find an optimal trading strategy that minimizes both the trading cost and the trading risk measured by quadratic variation. We contribute to the existing literature by considering a multi-dimensional geometric Brownian motion model for asset prices and proposing an efficient Markov chain approximation (MCA) approach to obtain the optimal trading trajectory. The MCA approach allows us not only to numerically compute the optimal strategy but also to theoretically analyse the influence of factors such as price impact, risk aversion and initial asset price on the optimal strategy, providing both quantitative and qualitative guidance on the trading behaviour. Numerical results verify the theoretical conclusions in the paper. They further illustrate the effects of cross impact and correlations on the optimal execution strategy in a multi-asset liquidation problem.

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基于马尔可夫链近似方法的最优投资组合执行

我们研究了在短时间内执行大型多资产投资组合的问题，目标是找到一种最优的交易策略，使交易成本和交易风险最小化，交易风险由二次方差度量。我们通过考虑资产价格的多维几何布朗运动模型，并提出了一种有效的马尔可夫链近似（MCA）方法来获得最优交易轨迹，从而对现有文献做出了贡献。MCA方法不仅可以用数字计算最优策略，还可以从理论上分析价格影响、风险规避和初始资产价格等因素对最优策略的影响，为交易行为提供定量和定性指导。数值结果验证了本文的理论结论。它们进一步说明了交叉影响和相关性对多资产清算问题中最优执行策略的影响。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

IMA Journal of Management Mathematics OPERATIONS RESEARCH & MANAGEMENT SCIENCE-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

4.70

自引率

17.60%

发文量

审稿时长

>12 weeks

期刊介绍： The mission of this quarterly journal is to publish mathematical research of the highest quality, impact and relevance that can be directly utilised or have demonstrable potential to be employed by managers in profit, not-for-profit, third party and governmental/public organisations to improve their practices. Thus the research must be quantitative and of the highest quality if it is to be published in the journal. Furthermore, the outcome of the research must be ultimately useful for managers. The journal also publishes novel meta-analyses of the literature, reviews of the "state-of-the art" in a manner that provides new insight, and genuine applications of mathematics to real-world problems in the form of case studies. The journal welcomes papers dealing with topics in Operational Research and Management Science, Operations Management, Decision Sciences, Transportation Science, Marketing Science, Analytics, and Financial and Risk Modelling.