Abstract
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.
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