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中国管理科学 ›› 2025, Vol. 33 ›› Issue (8): 14-25.doi: 10.16381/j.cnki.issn1003-207x.2023.1408

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随机市场深度下基于风险管理和交易约束的最优执行问题

吴伟平1,2,3, 林雨4, 金成能5,6,7, 唐振鹏8()   

  1. 1.福州大学经济与管理学院,福建 福州 350108
    2.福州大学福建经济高质量发展研究中心,福建 福州 350108
    3.福建省金融科技创新重点实验室,福建 福州 350108
    4.集美大学财经学院,福建 厦门 361021
    5.上海财经大学信息管理与工程学院,上海 200433
    6.顺丰科技有限公司,广东 深圳 518063
    7.浙江大学管理学院,浙江 杭州 310058
    8.福建农林大学经济与管理学院,福建 福州 350002
  • 收稿日期:2023-08-23 修回日期:2024-03-20 出版日期:2025-08-25 发布日期:2025-09-10
  • 通讯作者: 唐振鹏 E-mail:zhenpt@126.com
  • 基金资助:
    国家自然科学基金项目(72201067);国家自然科学基金项目(71973028)

Constrained Optimal Risk Sensitive Execution Problem with Stochastic Market Depth

Weiping Wu1,2,3, Yu Lin4, Chengneng Jin5,6,7, Zhenpeng Tang8()   

  1. 1.School of Economics and Management,Fuzhou University,Fuzhou 350108,China
    2.Fujian High-quality Economic Development Research Center,Fuzhou University,Fuzhou 350108,China
    3.The Fujian Provincial Key Laboratory of Fintech Innovation,Fuzhou 350108,China
    4.School of Finance and Economics,Jimei University,Xiamen 361021,China
    5.School of Information Management and Engineering,Shanghai University of Finance and Economics,Shanghai 200433,China
    6.SF Technology Co. ,Ltd. ,Shenzhen 518063,China
    7.School of Management,Zhejiang University,Hangzhou 310058,China
    8.School of Economics and Management,Fujian Agriculture and Forestry University,Fuzhou 350002,China
  • Received:2023-08-23 Revised:2024-03-20 Online:2025-08-25 Published:2025-09-10
  • Contact: Zhenpeng Tang E-mail:zhenpt@126.com

摘要:

最优执行问题作为一类投资决策问题,是金融学术界和实务界都广泛关注的热点话题之一。同时,随机市场流动性、投资者厌恶执行风险以及交易行为受监管限制这三个现实因素显著影响了交易执行策略。故本文基于随机市场深度假设,探究具有常数绝对风险厌恶(CARA)投资者在交易约束制约下的最优执行问题,依据限价订单簿(LOB)市场动态构建随机市场深度下基于风险管理和交易约束的最优执行模型,并利用动态规划方法给出最优执行策略的解析表达式。结果表明,理性投资者不会同时下达相反方向的订单,且最优策略是关于剩余订单量的分段线性函数。数值算例显示,较之风险中性投资者,风险厌恶型投资者为规避风险,倾向于在交易初期执行大规模订单。此外,本文模型在有效管理资产价格变动风险和流动性随机波动风险的同时,还提升了执行策略的有效性。且市场深度和交易约束显著影响了交易执行风险和策略的有效性。研究结果凸显了在解决风险厌恶型投资者的最优执行问题时,同时考虑随机市场流动性和交易约束的重要性。

关键词: 限价订单簿, 随机市场流动性, 最优执行问题, 常数绝对风险厌恶效用, 双边交易

Abstract:

As an investment decision-making problem, the optimal execution problem is a topic of considerable interest among finance scholars and professionals. Simultaneously, these realistic factors—stochastic market liquidity, investors' aversion to execution risk, and regulatory restrictions on trading behavior—all significantly influence the optimal trading strategies. Therefore, building on the assumption of stochastic market depth, the optimal execution problem with trading constraints encountered by investors exhibiting constant absolute risk aversion (CARA) utility is investigated. Following the market dynamics of the limit order book (LOB), an optimal execution model is constructed, taking into account risk management and trading constraints. Subsequently, an analytic execution strategy is presented using the dynamic programming approach. The results show that rational investors avoid placing orders in opposite directions simultaneously, and the optimal strategy is characterized by a piecewise linear function of the remaining order quantity. The numerical examples suggest risk-averse investors tend to execute large orders early in the trading period to avoid risk, compared to risk-neutral investors. Furthermore, aside from effectively managing the risk of asset price changes and stochastic fluctuations in liquidity, this model has also proven its capability to enhance the effectiveness of execution strategies. Additionally, market depth and trading constraints play significant roles in influencing both execution risk and the effectiveness of the strategy. In summary, the results emphasize the importance of accounting for both stochastic market liquidity and trading constraints when addressing the optimal execution problem for risk-averse investors.

Key words: limit order book, stochastic market liquidity, optimal execution problem, CARA utility, two-sided trading

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