Equilibrium and Precommitment Mean-Variance Portfolio Selection Problem with Partially Observed Price Index and Multiple Assets

  • Guohui GuanEmail author


In this paper, we aim to investigate the mean-variance portfolio selection in an economy with inflation risk. In the financial market, the inflation index can only be partially observed by a signal process. We transform the initial problem into an equivalent completely observed problem. The effect of the partially observed price index on the optimization problem is twofold. Firstly, the equivalent completely observed problem involves more estimation error. Secondly, the mean-variance criterion is distorted. Higher moment is assigned with a bigger weight. The optimization goal does not satisfy the assumption in the Bellman’s optimality condition and we derive the equilibrium strategy based on the extended HJB equation. Besides, we also show the results of the efficient frontier and strategy in the precommitment case. In the end of this paper, we present a sensitivity analysis to show the economic behaviors of the investor and compare the efficient strategies and frontiers in precommitment case and equilibrium case.


Inflation risk Investment Partially observation Time-consistent Precommitment Mean-variance 

Mathematics Subject Classification (2010)

49L20 90B85 91G10 


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The author is supported by fund for building world-class universities (disciplines) of Renmin University of China, the Fundamental Research Funds for the Central Universities, the China Postdoctoral Science Foundation Funded Project (Project No.:2018M640212), and the Research Funds of Renmin University of China.


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Authors and Affiliations

  1. 1.Center for Applied StatisticsRenmin University of ChinaBeijingChina
  2. 2.School of StatisticsRenmin University of ChinaBeijingChina

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