基于修正Black-Scholes金融市场和下方风险测度的动态投资组合优化

管理评论 ›› 2021, Vol. 33 ›› Issue (3): 14-28.

基于修正Black-Scholes金融市场和下方风险测度的动态投资组合优化

王秀国¹, 伍慧玲²

1. 中央财经大学统计与数学学院, 北京 100081;
2. 中央财经大学中国精算研究院, 北京 100081

收稿日期:2018-11-05 出版日期:2021-03-28 发布日期:2021-04-06
通讯作者: 王秀国(通讯作者),中央财经大学统计与数学学院教授,博士
作者简介:伍慧玲,中央财经大学中国精算研究院研究员,博士生导师,博士。
基金资助:
国家自然科学基金面上项目（11671411）；中央高校基本科研业务费专项资金；中央财经大学科研创新团队支持计划资助。

Dynamic Portfolio Optimization Based on Downside Risk Measures in the Modified Black-Scholes Financial Market

Wang Xiuguo¹, Wu Huiling²

1. School of Statistics and Mathematics, Central University of Finance and Economics, Beijing 100081;
2. China Institute for Actuarial Science, Central University of Finance and Economics, Beijing 100081

Received:2018-11-05 Online:2021-03-28 Published:2021-04-06

摘要/Abstract

摘要： 在修正的Black-Scholes金融市场下，研究了基于CVaR和CCaR下方风险测度的连续时间投资组合优化问题。给出了最优投资策略和有效前沿的显式表达式，其中最优投资策略就是投资于无风险资产和一种“风险资产”等波动率投资组合的组合，可解释为两基金分离定理。如果投资者事先给出风险资产的风险暴露，则不需要估计期望收益率参数，投资者的最优投资策略就可以通过估计出的波动率矩阵确定出来，这有效地解决了传统投资组合优化的最优权重由于估计期望收益率所产生的敏感性问题。进一步，利用本文提出的分析方法研究了均值-方差模型的最优投资策略和有效前沿。最后，实证分析表明，与不受估计期望收益率影响的两种经典投资策略（等权重投资策略和最小方差投资策略）相比较，本文构建的最优投资策略的组合权重随时间是平稳的，并具有更好的业绩表现。

关键词: 投资组合优化, 下方风险测度, 修正Black-Scholes金融市场, 投资策略, 有效前沿

Abstract: In the modified Black-Scholes financial market, this paper investigates continuous-time portfolio optimization problems based on CVaR and CCaR risk measures. The expressions of the optimal investment strategies and the efficient frontiers are obtained in closed form. The optimal investment strategies exhibit two-fund separation theorem which includes the riskless asset and equal-volatility portfolio. If the risk exposure of the risky assets is given by the investors in advance, then the optimal investment strategy can be determined by an estimated volatility matrix, without knowing the parameters of expected return. Hence, the sensitive problem brought by the traditional optimal portfolio weight in estimating the expected returns is solved efficiently. Moreover, the optimal investment strategy and the efficient frontier of the mean-variance model are derived by using our proposed method. Finally, the empirical analysis shows that our optimal portfolio weights are stable over time and obtain a significantly better performance than the equal-weight investment strategy and the minimum variance investment strategy, both of which are not influenced by the estimation of the expected returns.

Key words: portfolio optimization, downside risk measure, modified Black-Scholes financial market, investment strategy, efficient frontier

王秀国, 伍慧玲. 基于修正Black-Scholes金融市场和下方风险测度的动态投资组合优化[J]. 管理评论, 2021, 33(3): 14-28.

Wang Xiuguo, Wu Huiling. Dynamic Portfolio Optimization Based on Downside Risk Measures in the Modified Black-Scholes Financial Market[J]. Management Review, 2021, 33(3): 14-28.

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