Time-consistent investment strategy under partial information |
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| Affiliation: | 1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, PR China;2. School of Economics and Management, University of Chinese Academy of Sciences, Beijing 100190, PR China;3. Department of Economics and International Trade, Guangdong University of Finance, Guangzhou 510521, PR China;1. China Institute for Actuarial Science, Central University of Finance and Economics, Beijing 100081, PR China;2. Department of Applied Finance and Actuarial Studies, Faculty of Business and Economics, Macquarie University, Sydney, NSW 2109, Australia;3. Department of Statistics and Actuarial Science, The University of Hong Kong, Hong Kong, China;1. Department of Computing Science, School of Mathematics and Statistics, Xi''an Jiaotong University, 710049 Xi''an, Shaanxi, PR China;2. Rowe School of Business, Dalhousie University, 6100 University Avenue, Halifax, Canada B3H3J5;1. School of Science, Tianjin University, Tianjin 300072, PR China;2. Center for Applied Mathematics, Tianjin University, Tianjin 300072, PR China;1. School of Science, Tianjin University, Tianjin 300072, PR China;2. Center for Applied Mathematics, Tianjin University, Tianjin 300072, PR China;1. Lingnan (University) College, Sun Yat-sen University, Guangzhou 510275, PR China;2. School of Science, Tianjin University, Tianjin 300072, PR China;3. School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510520, PR China |
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| Abstract: | This paper considers a mean–variance portfolio selection problem under partial information, that is, the investor can observe the risky asset price with random drift which is not directly observable in financial markets. Since the dynamic mean–variance portfolio selection problem is time inconsistent, to seek the time-consistent investment strategy, the optimization problem is formulated and tackled in a game theoretic framework. Closed-form expressions of the equilibrium investment strategy and the corresponding equilibrium value function under partial information are derived by solving an extended Hamilton–Jacobi–Bellman system of equations. In addition, the results are also given under complete information, which are need for the partial information case. Furthermore, some numerical examples are presented to illustrate the derived equilibrium investment strategies and numerical sensitivity analysis is provided. |
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| Keywords: | Time inconsistency Mean–variance Partial information Equilibrium strategy Extended HJB system of equations |
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