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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2023, Vol. 40 ›› Issue (5): 751-762.doi: 10.3969/j.issn.1005-3085.2023.05.005

• • 上一篇    下一篇

基于随机规划的多期投资组合决策研究

玄海燕1,  姚存留2,  李鸿渐2,  安  蓉2,  钟嘉毅1   

  1. 1. 广州工商学院商学院，广州 810850;
    2. 兰州理工大学经济管理学院，兰州 730050
  • 收稿日期:2021-04-03 接受日期:2022-04-01 出版日期:2023-10-15 发布日期:2023-12-15
  • 通讯作者: 钟嘉毅 E-mail: 281099022@qq.com
  • 基金资助:
    国家自然科学基金(11261031)；广东省哲学社会科学项目(GD21CYJ05)；广州工商学院项目(KAZX2021109; KA202110).

Research on Multi-period Portfolio Decision Based on Stochastic Programming

XUAN Haiyan1,  YAO Cunliu2,  LI Hongjian2,  AN Rong2,  ZHONG Jiayi1   

  1. 1. Business School, Guangzhou College of Technology and Business, Guangzhou 810850;
    2. School of Economics and Management, Lanzhou University of Technology, Lanzhou 730050
  • Received:2021-04-03 Accepted:2022-04-01 Online:2023-10-15 Published:2023-12-15
  • Contact: J. Zhong. E-mail address: 281099022@qq.com
  • Supported by:
    The National Natural Science Foundation of China (11261031); the Philosophy and Social Sciences of Guangdong Province (GD21CYJ05); the Project of Guangzhou College of Technology and Business (KAZX2021109; KA202110).

摘要：

最优投资决策是投资者从长远角度出发，在复杂多变的环境中对风险资产进行合理配置，以获得最大的期望效用。研究了在多期投资时收益率不确定条件下的投资决策问题。首先，根据风险资产的历史数据建立ARMA-GARCH模型对资产的未来收益率预测，使用蒙特卡罗模拟法模拟收益率未来可能发生的情形，利用随机取样法搭建情景树。其次，在情景树的基础上，根据随机规划理论将Markowitz提出的均值–方差模型推广到多期。最后，选取中国证券市场上六只股票数据对模型进行实证研究。研究结果发现：情景树在描述不确定性问题上是有效的，提出的模型适用于多期投资，并能够给激进型、稳健型和保守型的投资者提供直观、明确的投资决策指导。

关键词: 随机规划, 多期投资组合, 情景树, 均值–方差模型, ARMA-GARCH模型

Abstract:

Optimal investment decision is an investor's rational allocation of risky assets in a complex and volatile environment from a long-term perspective in order to obtain the maximum desired utility. In this paper, the investment decision-making problem with uncertain rate of return in multi-stage investment is studied. Firstly, the ARMA-GARCH model is established to forecast the future rate of return of assets based on historical data of risky assets, Monte Carlo simulation method is used to simulate the possible future situation of yield, and random sampling is applied to build scenario trees. Secondly, based on the scenario tree, the mean-variance model proposed by Markowitz is extended to multiple periods according to stochastic programming theory. Finally, the data of six stocks in the Chinese securities market is selected to empirically investigate the model. The results of the study find that scenario tree is effective in describing the uncertainty problem. The model is suitable for multi-period investment and can provide radical, stable and conservative investors with intuitional and clear investment decision guidance.

Key words: stochastic programming, multi-period investment portfolio, scenario tree, mean-variance model, ARMA-GARCH model

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