基于在线算法的改进指数梯度投资组合策略

doi:10.16381/j.cnki.issn1003-207x.2019.1857

中国管理科学 ›› 2022, Vol. 30 ›› Issue (9): 49-60.doi: 10.16381/j.cnki.issn1003-207x.2019.1857cstr: 32146.14.j.cnki.issn1003-207x.2019.1857

基于在线算法的改进指数梯度投资组合策略

张永¹, 龙婉容¹, 杨兴雨¹, 张卫国²

1.广东工业大学管理学院，广东广州510520；2.华南理工大学工商管理学院，广东广州510640

收稿日期:2019-11-15 修回日期:2020-04-16 出版日期:2022-09-20 发布日期:2022-09-01
通讯作者: 杨兴雨(1981-)，男(汉族)，河南南阳人，广东工业大学管理学院，教授，博士，硕士生导师，研究方向：金融工程与在线金融决策，Email：yangxy@gdut.edu.cn. E-mail:yangxy@gdut.edu.cn
基金资助:
教育部人文社会科学研究基金资助项目(21YJA630117)；广东省哲学社会科学规划项目(GD19CGL06)

Improved Exponential Gradient Portfolio Strategy Based on Online Algorithm

ZHANG Yong¹, LONG Wan-rong¹, YANG Xing-yu¹, ZHANG Wei-guo²

1. School of Management，Guangdong University of Technology，Guangzhou 510520，China；2. School of Business Administration，South China University of Technology，Guangzhou 510641，China

Received:2019-11-15 Revised:2020-04-16 Online:2022-09-20 Published:2022-09-01
Contact: 杨兴雨 E-mail:yangxy@gdut.edu.cn

摘要/Abstract

摘要： 弱集成算法是对专家意见进行动态加权平均的在线学习算法。近年来，机器学习和人工智能等方法被用来研究在线投资组合问题。该文从弱集成算法的在线学习及其序列决策性角度出发，设计改进的指数梯度在线投资组合策略，以弥补指数梯度在线投资组合策略不能结合交易费用进行分析的缺陷。首先根据指数梯度在线投资组合策略的更新方法构建代表投资策略的专家意见池，并以此为基础应用弱集成算法加权集成专家意见得到改进的指数梯度在线投资组合策略，证明了该策略可与最优专家策略(基准策略)相媲美。其次将交易费用引入到改进的指数梯度在线投资组合策略中，进一步给出对应的投资策略，重要的是理论上证明了该策略实现的平均累积收益与最优专家策略实现的平均累积收益之间的差值存在渐进式下界，从而提高了指数梯度在线投资组合策略的实用性。最后利用国内外股票市场的历史数据进行实证分析，说明了改进的指数梯度在线投资组合策略的可行性和有效性。

关键词: 在线学习；专家意见；在线投资组合；交易费用；累积收益

Abstract: The weak aggregating algorithm is an online learning algorithm that dynamically weights the average of expert advice. In recent years, machine learning and artificial intelligence have been used to study online portfolio. An important feature of online portfolio strategy is that it does not make any statistical assumptions about stock prices, constructs an investment strategy based on historical data, and ensures that its cumulative gains are almost as good as benchmark strategy. Under the perspective of online sequence decision of weak aggregating algorithm, an improved exponential gradient portfolio strategy is designed, which is made up for the defeat that exponential gradient online portfolio strategy can not be combined with transaction costs. Firstly, according to the update method of exponential gradient online portfolio strategy, the expert advice pool representing the investment strategy is constructed, and on this basis, the weak aggregating algorithm is used to obtain the improved exponential gradient online portfolio strategy, which has proved to be competitive. Secondly, transaction costs are introduced into the improved exponential gradient online portfolio strategy, and the improved exponential gradient online portfolio strategy with transaction costs is further proposed. Significantly, it is theoretically proved that there is an asymptotical lower bound on the difference between the average of cumulative gain of the strategy and the best expert advice, so as to improve the practicability of exponential gradient online portfolio strategy effectively. Finally, an empirical analysis on historical stock data is utilized to test the performance of improved exponential gradient strategy. On these data, anexperimentisprovided to illustrate the feasibility as well as effectiveness of the strategy. Whether or not transaction costs are taken into account, the improved exponential gradient portfolio strategy performswell and achieves competitive performance in practical applications. Moreover, the empirical results showthatthe proposedstrategynotonlyperforms well in terms of returnbut also strikes a good balance betweenreturn and risk.

Key words: online learning; expert advice; online portfolio selection; transaction costs; cumulative gains

中图分类号:

F830

张永,龙婉容,杨兴雨, 等. 基于在线算法的改进指数梯度投资组合策略[J]. 中国管理科学, 2022, 30(9): 49-60.

ZHANG Yong,LONG Wan-rong,YANG Xing-yu, et al. Improved Exponential Gradient Portfolio Strategy Based on Online Algorithm[J]. Chinese Journal of Management Science, 2022, 30(9): 49-60.

参考文献

［1］ Markowitz H. Portfolio selection［J］. Journal of Finance, 1952, 7(1): 77-91.
［2］陈收, 杨宽, 廖懿, 等.证券市场中股票成交量对投资组合优化的影响［J］.管理科学学报, 2002, 5(5): 6-10.Chen Shou, Yang Kuan, Liao Yi, et al. Trade volume’s impact on efficient frontier of portfolio selection［J］.Journalof Management ScienceinChina, 2002, 5(5): 6-10.
［3］ Bielecki T R, Jin Hanqing, Pliska S R, etal. Continuous-time mean-variance portfolio selection with bankruptcy prohibition［J］. Mathematical Finance, 2005, 15(2): 213-244.
［4］ Basak S,Chabakauri G. Dynamic mean-variance asset allocation［J］. Review of Financial Studies, 2010, 23(8): 2970-3016.
［5］张鹏, 张卫国, 张逸菲.具有最小交易量限制的多阶段均值-半方差投资组合优化［J］.中国管理科学, 2016, 24(7): 11-17.Zhang Peng, Zhang Weiguo, Zhang Yifei. Multi-period mean-semivarian ceport folio selection with minimum transactionlo tscons traints［J］. Chinese Journal of Management Science, 2016, 24(7): 11-17.
［6］李斌, 张迪, 冯佳捷.序列相关性在资产组合绩效改善中的作用［J］.管理科学, 2018, 31(4): 148-160.Li Bin, Zhang Di, Feng Jiajie. The effect of serial dependence on improving portfolios’ performance［J］. Journal of Management Science, 2018, 31(4): 148-160.
［7］李爱忠, 汪寿阳, 彭月兰.考虑随机利率和通货膨胀的连续时间资产组合选择［J］.中国管理科学, 2019, 27(2): 61-70.Li Aizhong, Wang Shouyang, Peng Yuelan. Continuous-time asset allocation strategy with inflation and stochastic interest rates［J］. Chinese Journal of Management Science, 2019, 27(2): 61-70.
［8］ Cover T M. Universal portfolios［J］. Mathematical Finance, 1991, 1(1): 1-29.
［9］李斌, 张迪, 唐松慧.基于次梯度投影的泛投资组合选择策略［J］.管理科学学报, 2018, 21(3): 94-104.Li Bin, Zhang Di, Tang Songhui. Universal portfolio selection strategy based on sub-gradient projection［J］. Journal of Management Sciences in China, 2018, 21(3): 94-104.
［10］ O’ Sullivan P, Edelman D. Adaptive universal portfolios［J］. European Journal of Finance, 2015, 21(4): 337-351.
［11］ Hazan E, Kale S. An online portfolio selection algorithm with regret logarithmic in price variation［J］. Mathematical Finance, 2015, 25(2): 288-310.
［12］ Borodin A, El-Yaniv R, Gogan V. Can we learn to beat the best stock［J］. Journal of Artificial Intelligence Research, 2004, 21: 579-594.
［13］ Li Bin, Zhao Peilin, Hoi S C H, et al. PAMR: Passive aggressive mean reversion strategy for portfolio selection［J］. Machine Learning, 2012, 87(2): 221-258.
［14］ Li Bin, Hoi S C H, Zhao Peilin, et al. Confidence weighted mean reversion strategy for online portfolio selection［J］. ACM Transactions on Knowledge Discovery from Data, 2013, 7(1): 4:1-4:38.
［15］ Li Bin, Hoi S C H, Sahoo D, et al. Moving average reversion strategy for on-line portfolio selection［J］. Artificial Intelligence, 2015, 222: 104-123.
［16］ Huang Dingjiang, Yu Shunchang, Li Bin, et al. Combination forecasting reversion strategy for online portfolio selection［J］. ACM Transactions on Intelligent Systems and Technology, 2018, 9(5): 58:1-58:22.
［17］ Chu Gang, Zhang Wei, Sun Guofeng, et al. A new online portfolio selection algorithm based on kalman filter and anti-correlation［J］. Physica A, 2019, DOI:10.1016/j.physa.2019.04.185.
［18］ Helmbold D P, Schapir R E, Singer Y, et al. On-line portfolio selection using multiplicative updates［J］. Mathematical Finance, 1998, 8(4): 325-347.
［19］彭子衿, 徐维军.基于股价预测的泛证券投资组合策略［J］.中国管理科学, 2018, 26(9): 1-10.Peng Zijin, Xu Weijun. Universal portfolio strategy based on forecasting price［J］. Chinese Journal of Management Science, 2018, 26(9): 1-10.
［20］ Zhang Weiguo, Zhang Yong, Yang Xingyu, et al. A class of on-line portfolio selection algorithms based on linear learning［J］. Applied Mathematics and Computation, 2012, 218(24): 11832-11841.
［21］ Guan Hao, An Zhiyong. A local adaptive learning system for online portfolio selection［J］. Knowledge-Based Systems, 2019, 186(15): 104958.1-104958.10.
［22］ Li Bin, Hoi S C H, Gopalkrishnan V. CORN: Correlation-driven nonparametric learning approach for portfolio selection［J］. ACM Transactions on Intelligent Systems and Technology, 2011, 2(3): 21:1-21:29.
［23］ Blum A, Kalai A. Universal portfolios with and without transaction costs［J］. Machine Learning, 1999, 35(3): 193-205.
［24］刘善存, 邱菀华, 汪寿阳.带交易费用的泛证券组合投资策略［J］.系统工程理论与实践, 2003, 23(1): 22-25.Liu Shancun, Qiu Wanhua, Wang Shouyang. Universal portfolio selection with transaction costs［J］. Systems Engineering-Theory & Practice, 2003, 23(1): 22-25.
［25］ Tunc S, Donmez M A, Kozat S S. Optimal investment under transaction costs: A threshold rebalanced portfolio approach［J］. IEEE Transactions on Signal Processing, 2013, 61(12): 3129-3142.
［26］ Albeverio S, Lao Lanjun, Zhao Xuelei. On-line portfolio selection strategy with prediction in the presence of transaction costs［J］. Mathematical Methods of Operations Research, 2001, 54(1): 133-161.
［27］ Li Bin, Wang Jialei, Huang Dingjiang, et al. Transaction cost optimization for online portfolio selection［J］. Quantitative Finance, 2017, 18(8): 1411-1424.
［28］ Kalnishkan Y, Vyugin M V. The weak aggregating algorithm and weak mixability［J］. Journal of Computer and System Sciences, 2008, 74(8): 1228-1244.
［29］ Levina T, Levin Y, Mcgill J, et al. Weak aggregating algorithm for the distribution-free perishable inventory problem［J］. Operations Research Letters, 2010, 38(6): 516-521.
［30］张永, 张卫国, 徐维军, 等.集成有限个专家意见的在线投资组合策略［J］.系统工程理论与实践, 2015, 35(1): 57-66.Zhang Yong, Zhang Weiguo, Xu Weijun, et al. Online portfolio selection strategy by aggregating finite expert advices［J］. Systems Engineering-Theory & Practice, 2015, 35(1): 57-66.
［31］杨兴雨, 刘悦, 杨晓光, 等.带交易费用的集成专家意见在线投资组合策略［J］.系统工程理论与实践, 2018, 38(8): 1946-1959.Yang Xingyu, Liu Yue, Yang Xiaoguang, et al. Online portfolio selection strategy of aggregating expert advice with transaction costs［J］. Systems Engineering-Theory & Practice, 2018, 38(8): 1946-1959.

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基于在线算法的改进指数梯度投资组合策略

Improved Exponential Gradient Portfolio Strategy Based on Online Algorithm

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