基于在线学习算法的投资组合选择问题研究

发布时间：2018-05-14 00:29

本文选题：在线学习 + 投资组合选择　；参考：《华东理工大学》2017年硕士论文

【摘要】：在线学习是近二十年来机器学习领域热门的研究分支,其主要特点是能够根据线上实时数据反馈及时对模型进行自我改进和优化,能够保证模型在当前历史数据下达到最优目标值或最小损失,目前已被广泛应用于信息和金融等领域。特别地,由于证券投资组合选择问题中的股票价格具有时序性,因而可以利用在线学习算法进行有效处理。近年来,基于在线学习的在线投资组合选择已成为机器学习和人工智能领域热门的研究方向之一。许多学者提出了一系列有效的在线投资组合选择策略,如经典的泛化策略(UP)、指数更新策略(EG)等等。但是此类投资组合算法常常会忽略交易成本问题,因而造成算法在实际应用中效果不佳。为了解决这一问题,本论文将从在线学习算法和投资组合交易成本的角度进行研究。论文首先讨论了不同损失函数下的在线学习算法的特性;然后设计了两类新的在线投资组合算法用以解决在线投资组合选择问题中的交易成本计算问题。第一类是针对Cover经典的UP策略会在每一期都进行资产交易因而产生较高的交易成本问题,本文提出了基于竞争性在线算法思想的一类交易成本下的半泛化投资组合策略,简称SUP策略。SUP策略的基本思想是根据交易成本来选择交易频率,根据历史数据选择当期的交易量。在投资组合问题中,我们可以认为SUP是在考虑交易成本的情况下,对于投资收益高于交易成本的情况进行交易,反之则不进行投资组合交易。我们在理论上证明了 SUP策略的泛化性质及其损失上界k ln(n)+ O(k+1)。为了实现这一策略,我们设计了在线因子图和随机游走两个算法进行近似求解,并考察了在NYSE和SP500两个实际数据集上的累积收益和换手率等金融指标,实验结果表明该策略较好地解决了交易成本问题,在交易成本不断增加的情况下,取得了比以往UP等策略更优的结果。第二类是基于牛顿迭代算法思想提出了基于交易成本的在线牛顿步算法,简称ONS-Cost策略,该策略的基本思想是利用损失函数的二阶信息进行迭代,其中损失函数由对数累积收益和交易成本损失项组成。在投资组合选择问题中,此类算法可以根据损失函数自动控制投资组合的交易频率,在提升投资收益的同时降低交易成本。我们利用牛顿迭代算法实现ONS-Cost策略,从实验效果上来看,随着交易成本增加,相比于ONS策略,ONS-Cost策略的累积净收益下降缓慢,投资收益良好。本文的研究不仅对计算金融领域中在线投资组合选择策略研究具有一定的理论意义,对金融工业界中实际投资组合策略的构造也具有一定的指导性作用。
[Abstract]:Online learning is a hot research branch in the field of machine learning in recent 20 years. Its main characteristic is that it can improve and optimize the model in time according to the on-line real-time data feedback. It can ensure that the model can reach the optimal target value or minimum loss in the current historical data, so it has been widely used in the field of information and finance. In particular, because the stock price in portfolio selection problem is time-series, online learning algorithm can be used to deal with it effectively. In recent years, online portfolio selection based on online learning has become one of the hot research directions in the field of machine learning and artificial intelligence. Many scholars have put forward a series of effective online portfolio selection strategies, such as classic generalization strategy, index updating strategy (EGG) and so on. However, this kind of portfolio algorithm often ignores the transaction cost problem, which results in poor performance in practical application. In order to solve this problem, this paper will study the online learning algorithm and portfolio transaction cost. This paper first discusses the characteristics of online learning algorithm under different loss functions, and then designs two new online portfolio algorithms to solve the transaction cost calculation problem in online portfolio selection problem. The first is to solve the problem of high transaction cost caused by the classic up strategy of Cover. This paper proposes a semi-generalized portfolio strategy under transaction cost based on competitive online algorithm. The basic idea of SUP strategy. Sup strategy is to select the transaction frequency according to the transaction cost and to select the current trading volume according to the historical data. In the portfolio problem, we can think that SUP is to deal with the case where the investment income is higher than the transaction cost when the transaction cost is taken into account, otherwise, the portfolio transaction is not carried out. We prove theoretically the generalization property of SUP strategy and its loss upper bound k lnn ~ n) k ~ (1). In order to realize this strategy, we design online factor graph and random walk algorithm to solve the problem approximately, and investigate the financial indexes such as cumulative income and turnover rate on two real data sets of NYSE and SP500. The experimental results show that the strategy can solve the problem of transaction cost, and the result is better than that of the previous up strategy when the transaction cost is increasing. The second kind is based on Newton iterative algorithm. An online Newton step algorithm based on transaction cost is proposed, which is referred to as ONS-Cost strategy. The basic idea of this strategy is to iterate by using the second order information of loss function. The loss function consists of logarithmic cumulative income and transaction cost loss. In the portfolio selection problem, this algorithm can automatically control the trading frequency of the portfolio according to the loss function, and reduce the transaction cost while increasing the investment income. We use Newton iterative algorithm to implement ONS-Cost strategy. As the transaction cost increases, compared with ONS strategy, the cumulative net income of ONS-Cost strategy decreases slowly and the investment returns are good. The research in this paper not only has certain theoretical significance to the research of online portfolio selection strategy in the field of computational finance, but also has a certain guiding effect on the construction of actual portfolio strategy in the financial industry.
【学位授予单位】：华东理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP181

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