均值-风险动态投资组合模型中时间一致性问题的理论和实证研究

The time consistency issue in dynamic portfolio selection models concerns whether the global optimal policy is also optimal (or efficient) for the local problem, which is an important topic in the portfolio selection area. This research aims to investigate the time consistency issue in mean-risk dynamic portfolio selection models from theoretical and empirical aspects. We consider two types of models: dynamic mean-VaR model and dynamic mean-variance model with constraints, which both violate time consistency requirement. For dynamic mean-VaR model, we will study efficient investment policy and investigate how the investor's risk attitude changing during the whole investment process. A better revised policy will be then proposed. For dynamic mean-variance model with constraints, we will focus on the relationship between time consistency (or time consistency in efficiency) and the constraints by using duality theory and arbitrage theory, and then find suitable set of constraints to eliminate (or weaken) time inconsistency. Finally, based on VaR, we will construct WVaR, which satisfies weak time consistency, and then compute the corresponding policy of dynamic mean-WVaR model by time inconsistent stochastic control method. And we will empirically compare the investment performance between the policy of dynamic mean-WVaR model and the revised policy of dynamic mean-VaR model. This research will help solving several difficult problems in the time consistency theory and propose new methods and techniques to amend dynamic portfolio selection models.

动态投资组合模型中的时间一致性问题是指全局最优投资策略是否仍然为局部问题的最优（或有效）策略，是投资组合研究中的重要课题。本项目旨在对动态均值?风险模型中时间一致性问题进行深入的理论和实证研究。研究主要涉及两类不满足时间一致性要求的模型：动态均值?VaR模型和带约束的动态均值?方差模型。对于动态均值?VaR模型，我们将从其有效投资策略出发，研究投资者的风险态度在投资过程中的变化规律，并基于此构造出更好的修正策略。对于带约束的动态均值?方差模型，我们则借助对偶理论和套利理论着重研究时间一致性（或有效性意义下的时间一致性）与约束条件的关系。最后，我们将基于VaR构造出满足弱时间一致性要求的风险度量WVaR，利用时间不一致随机控制方法计算均值?WVaR模型的策略，并实证比较该策略与均值?VaR模型修正策略的投资表现。本项目研究有望解决时间一致性理论中的若干困难问题，并提出新的模型修正方法和技术。

动态投资组合模型的时间不一致性问题是近年来投资组合研究中的热点问题。在资助项目执行期间，我们对动态均值−方差模型、动态均值-VaR模型、动态均值-CVaR模型、动态前景理论模型的时间不一致性问题进行了较为深入的研究。我们计算了带各种约束的动态均值-方差模型的最优策略，并据此研究了模型时间一致性与约束条件之间的联系，提出了通过添加合适的约束条件来解决模型时间不一致性的设想和方法；对具有分片财富依赖风险厌恶系数的动态均值-方差模型、动态均值-VaR模型、动态均值-CVaR模型、动态前景理论模型的全局最优策略进行了分析和实证研究，提出了计算各模型时间一致策略的方法，讨论了时间一致策略的性质和特点；提出利用mean-field控制方法求解动态均值-方差模型，为求解动态不可分投资问题提供了新的理论工具。