基于并行概率规划的股票指数模拟

Stock Index Simulation Based on Parallel Probabilistic Planning

在金融领域,股票指数(简称股指)模拟与分析是一个重要课题,用于股票市场的长期分析.然而,大多数的这类工作目前由专业的分析师来完成,非职业投资者难以涉及.另一方面,现有的基于数学或机器学习的股指模拟方法具有参数多、人工干预多、可解释性差等缺点.针对以上问题,本文基于并行概率规划(Parallel Probabilistic Planning,PPP),提出了一个股指模拟的规划领域模型,并能够进行自动求解.股票市场具有大量的不确定性和并发性,因此适合用并行概率模型来表示.方法的核心思想是将股指模拟问题转化为智能规划问题.首先,本文构建股指模拟问题的规划领域模型.由于股票市场的复杂性,需尽可能地考虑各种影响因素、约束条件、可能事件以及它们之间的关联.构建的规划领域模型由针对PPP的规划语言RDDL(Relational Dynamic Influence Diagram Language)来进行描述.接着,使用PPP的模拟求解工具——rddlsim来进行基于抽样的规划求解.rddlsim是国际概率规划大赛IPPC提供的求解工具,能够全面地解析RDDL描述.实验数据使用上证50指数和上证100指数的股票数据.即,从某个时间点开始,通过求解对应的规划问题来模拟未来一年股票指数的变化趋势.求解结果,一方面,与真实股票指数变化作对比;另一方面,与基于线性回归、基于SVM和基于LSTM的三种模拟方法的结果作对比.我们分别使用交叉熵、最小二乘和皮尔森相关系数作为损失函数.实验表明,本文的模拟效果比较贴近于真实的股指变化趋势;在大多数情况下,本文方法优于基于回归或SVM的模拟方法,且与基于LSTM的方法性能相当.并且,相对于对比的模拟方法,本文方法提供了较强的可解释性,且在求解过程中不需人工干预或调参.这是因为,形式化的规划领域描述展示了在股指模拟问题中各种因素如何相互影响,而且自动求解得到的规划解给出了导致模拟结果的状态变化轨迹.

In finance, the stock index simulation is an important topic, used for a long-term analysis of the stock market. However, most of this work has been done by professional analysts and it is difficult for non-professional investors to be involved in. On the other hand, existing simulation methods, either based on mathematical formulas or based on machine learning technologies, have some common shortcomings, such as too many parameters or continuous manual interventions, and poor interpretability. To solve the above problems, this paper proposed a planning domain model of stock index simulation and solved problem instances automatically with the built model, based on the PPP (Parallel Probabilistic Planning). Since the stock market has a plenty of the concurrency and the uncertainty, it is suitable to model it with some concurrent and probabilistic model. The core idea of our method was to transform a stock index simulation problem into an artificial planning problem. First, we built a planning domain model for the stock index simulation problem. It was necessary to express various influential factors, constraints, events and their correlations as many as possible due to the complexity of the stock market. The built model was described by the formal PPP language called the RDDL (Relational Dynamic Influence Diagram Language). Second, we used the PPP simulation tool - rddlsim to solve problem instances of the built model based on state sampling. The rddlsim is officially provided by the IPPC (International Probabilistic Planning Competition) and is able to analyze the RDDL description integrally. Our experiments used the stock data of the SSE 50 Index and the SSE 100 Index. Specially, since some time point, we simulated the movement of stock indices in the next year, by solving the corresponding planning problems. The solutions, on one hand, were compared with the real index movement;on the other hand, were compared with other three simulation methods, including the linear regression, the SVM (Support Vector Machine) and the LSTM (Long Short-Term Memory). We used the cross-entropy function, the least square function and the Pearson correlation coefficient as loss functions, respectively. The experimental results showed our simulation results were close to the real stock index movement. Furthermore, in most cases, our simulation results were better than those of the regression or SVM method, and almost equivalent to that of the LSTM method. However, compared to the other simulation methods mentioned above, our mothed provided a clearer interpretability and did not need any manual intervention or parameter adjustment. This is because, the formal planning domain definition indicates how all kinds of variables effect each other in this simulation problem, and the plan solution presents a state trajectory of the simulation result.