考虑交易成本的高维动态投资优化模型

Under the background of preventing economic and financial risks, Political Bureau of the CPC Central Committee has put forward six stabilization requirements, such as "investment stability" and "finance stability", to flexibly cope with the quick change of economic environment. As the main battlefield of economic transformation, how to make investment decisions in the presence of a large number of assets has become an interesting research topic, meanwhile, it brings a new challenge as well as a chance to investors/investment institutions. Transaction cost plays an important role in all investment activities. Compared to the explicit costs such as bid-ask spread or commission fees, implicit transaction costs caused by block transactions are more difficult to analyze. In this research proposal, we consider a multiperiod portfolio optimization model in the presence of general transaction costs, including implicit transaction costs when the dimension of asset returns is high. We analyze the theoretical properties of the optimal strategies, which are subsequently used to construct easy-to-implement heuristic trading strategies. We then extend the model to the case when the market is volatile and when the dimension of risky asset returns is high. More specifically, we first explore several theoretical properties of the optimal strategy, given that the optimal solution is not analytically available in the presence of general convex transaction costs. We then extend the model to the case when the asset returns are volatile. We propose a robust estimator of the precision matrix when there is contamination. Through extensive Monte Carlo simulation and empirical study, we show that the proposed estimator has superior out-of-sample performance. In the end, we consider the model when there are many risky assets. We will show analytically that considering different types of transaction costs is equivalent to constructing either sparse or stable portfolio especially when the asset returns dimension is high. We will show through extensive empirical study the importance of considering transaction costs in high dimensional portfolio selection.

在当下防范经济金融风险的大背景下，中央政治局提出了“稳投资”、“稳金融”等六稳要求，以期灵活应对经济形势的变化。而作为经济转型的主战场，如何在交易频繁及资产数目众多的资本市场中进行决策，成了投资优化领域的研究热点，同时也给投资者/机构的研究带来新的机遇和挑战。交易成本一直存在于各类投资活动中，和印花税或佣金等显性成本相比较，由大宗交易等带来的隐性成本因其难以刻画，因而鲜有文献对其进行研究。本课题旨在研究包括隐性成本的高维动态投资模型的理论及其算法应用。首先，在一般化的凸交易成本与高维资产情况下，根据最优策略的解析性质提出避免维数灾难的启发式算法，弥补对含有交易成本的投资模型框架的空缺及提供策略参考；其次，提出当数据含有奇异值时的精度矩阵估计量并将其应用到中国市场，从而提供更好的投资依据；最后，针对风险资产维数高的现状，构建交易成本与各类头寸的桥梁，从理论上证明交易成本在决策过程中的重要性。

作为经济转型的主战场，如何在交易频繁及资产数目众多的资本市场中进行决策，成了投资优化领域的研究热点，同时也给投资者/机构的研究带来新的机遇和挑战。首先，在资产众多的情况下，如何更好的解释收益率的来源；其次，交易成本一直存在于各类投资活动中，和印花税或佣金等显性成本相比较，由大宗交易等带来的隐性成本因其难以刻画，因而鲜有文献对其进行研究。在本课题中，我们首先研究了股票收益率的可解释性问题，然后探究包括了各类交易成本在内的投资优化模型对于构造稀疏以及稳定的投资头寸的作用，从理论和实证上证明交易成本在决策过程中的重要性。同时，在市场表现极度不稳定的状态下，我们提出了当数据中含有噪声时的精度矩阵估计量并将其应用到中国市场，为投资者提供更好的投资依据。