数学物理学报(英文版) ›› 2009, Vol. 29 ›› Issue (4): 817-828.doi: 10.1016/S0252-9602(09)60072-2

• 论文 • 上一篇    下一篇

MARKOWITZ STRATEGIES REVISED

严加安,周迅宇   

  1. Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, No. 55 Zhongguancun East Road, Beijing 100190, China；Nomura Centre for Mathematical Finance, and Oxford–Man Institute of Quantitative Finance, The University of Oxford, 24–29 St Giles, Oxford OX1 3LB, UK, and Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, Hong Kong
  • 收稿日期:2008-12-30 出版日期:2009-07-20 发布日期:2009-07-20
  • 基金资助:

    The work of Yan was supported by the National Natural Science Foundation of China (10571167), the National Basic Research Program of China (973 Program, 2007CB814902), and the Science Fund for Creative Research Groups (10721101); The work of Zhou was supported by the Nomura Centre for Mathematical Finance and the Oxford–Man Institute of Quantitative Finance, as well as a start-up fund of the University of Oxford.

MARKOWITZ STRATEGIES REVISED

 YAN Jia-An, ZHOU Xun-Yu   

  1. Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, No. 55 Zhongguancun East Road, Beijing 100190, China；Nomura Centre for Mathematical Finance, and Oxford–Man Institute of Quantitative Finance, The University of Oxford, 24–29 St Giles, Oxford OX1 3LB, UK, and Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, Hong Kong
  • Received:2008-12-30 Online:2009-07-20 Published:2009-07-20
  • Supported by:

    The work of Yan was supported by the National Natural Science Foundation of China (10571167), the National Basic Research Program of China (973 Program, 2007CB814902), and the Science Fund for Creative Research Groups (10721101); The work of Zhou was supported by the Nomura Centre for Mathematical Finance and the Oxford–Man Institute of Quantitative Finance, as well as a start-up fund of the University of Oxford.

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摘要：

Continuous-time Markowitz’s mean-variance efficient strategies are modified by parameterizing a critical quantity. It is shown that these parameterized Markowitz strategies could reach the original mean target with arbitrarily high probabilities. This, in turn, motivates the introduction of certain stopped strategies where stock holdings are
liquidated whenever the parameterized Markowitz strategies reach the present value of the mean target. The risk aspect of the revised Markowitz strategies are examined via expected discounted loss from the initial budget. A new portfolio selection model is suggested based on the results of the paper.

关键词: continuous-time portfolio selection, Markowitz efficient strategies, goal-reaching probability, stopping time, expected loss

Abstract:

Continuous-time Markowitz’s mean-variance efficient strategies are modified by parameterizing a critical quantity. It is shown that these parameterized Markowitz strategies could reach the original mean target with arbitrarily high probabilities. This, in turn, motivates the introduction of certain stopped strategies where stock holdings are
liquidated whenever the parameterized Markowitz strategies reach the present value of the mean target. The risk aspect of the revised Markowitz strategies are examined via expected discounted loss from the initial budget. A new portfolio selection model is suggested based on the results of the paper.

Key words: continuous-time portfolio selection, Markowitz efficient strategies, goal-reaching probability, stopping time, expected loss

中图分类号: 

  • 90A09
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