存在非流动性资产的连续时间投资组合选择问题：基于交易时间受限的视角

All the time, the research on the optimal investment strategy under illiquidity risk has been the common hotspot of financial industry and academic circles, but it is urgent to measure market liquidity from the perspective of trading times. Trading time restrictions are generally involved in non-traded assets, assets with random trading times, and the breakout of liquidity crises. In addition, there are another two important market features: an executive can directly influence the stock price of his own company with work effort; a fund manager can be compensated with a high-water mark contract. The existing literature has been restricted in the above single market feature. Accordingly, this project will propose three continuous-time portfolio choice models considering the above multiple features. The objective of this project is to study the optimal strategy for each multiple feature model, and focus on exploring the impact of illiquidity risk resulting from trading time restriction on the optimal strategy. In order to overcome difficulties caused by multiple features, this project will extend the stochastic control methods—dynamic programming method as well as numerical methods and theoretical analysis methods for partial differential equations—in the existing single feature models to the three multiple feature models. Besides, this project will provide the appearance and the analytic properties of the optimal strategies. This project will provide the theoretical evidence for the design and implementation of optimal incentive-based compensation schemes, and provide the scientific decision-making basis for investors.

关于非流动性风险影响下最优投资策略的研究一直以来都是理论金融界和实证金融界共同关注的热点问题，但急需从交易时间的角度来衡量金融资产的流动性问题。除由非交易性资产、随机交易时间资产和流动性危机发生等带来的交易时间约束外，现实金融市场还有两个重要特征：公司管理者可以通过工作投入影响本公司股价；对冲基金经理人可以依据高水位线条款获取业绩报酬。现有文献几乎都局限于考虑上述单因素情形，因此本项目将创建三个考虑上述多因素共存情形下的连续时间投资组合选择模型，旨在研究多因素共存情形下的最优策略，并重点探索由交易时间约束带来的非流动性风险对最优策略的影响。为了克服由多因素带来的困难，本项目将现有单因素模型中使用的随机控制方法——动态规划方法和偏微分方程的数值、理论分析方法推广到多因素模型中，给出最优策略的直观刻画和分析性质。本项目将为优化报酬激励方案的设计与实施提供理论依据，为投资者提供科学决策依据。

存在非流动性资产的投资组合选择问题一直以来都是理论金融界和实证金融界共同关注的热点问题，但急需从交易时间的角度来衡量金融资产的流动性问题。本项目创建了三个不同金融背景下的连续时间投资组合选择模型来探索：（1）由限制性股票带来的交易时间约束和工作投入双重因素对公司管理者最优投资策略的影响；（2）由最优停时边界带来的交易时间约束和高水位线条款双重因素对对冲基金经理人最优投资策略的影响；（3）由资本利得税纳税时机的选择和市场时机的选择引起的交易时机的选择对投资者最优投资策略的影响。本项目利用动态规划、偏微分方程的数值与理论分析、和数值模拟等方法给出了最优投资策略的直观刻画和分析性质，并着重分析了由交易时间约束带来的非流动性风险对最优投资策略的影响。本项目的研究发现：（1）限制性股票能激励公司管理者努力工作来提高公司业绩，且当越来越靠近限制性股票行权日时，公司管理者提高公司业绩的激励效应将会增大。（2）当基金价值越来越接近高水位线时，基金经理人将被激发更多的工作投入；基金经理人更喜欢较高的管理费，但可能更喜欢较低的激励费。（3）收益可预测性与资本利得税并存时的最优策略有助于缓解纳税时机选择和市场时机选择之间的矛盾关系；收益可预测性可以显著增加因资本利得税导致的效用损失和由延迟实现资本利得而获得的税金时间价值。本项目不仅可以为优化报酬激励方案的设计与实施提供理论依据，而且可以为投资者运用金融资产、市场时机进行投资获利、套期保值、风险防范和合理避税等提供科学决策依据。