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In this paper, we consider the optimal investment control problem for a company who worries about inflation risk. We assume that the company is self-financing. The decision maker of the company can invest in a financial market consisting of two assets: one risk-free asset, one risky asset. Our purpose is to find the impacts of inflation on optimal investment policy. With the objective of maximizing the CRRA utility of terminal wealth, the closed-form solutions of the optimal investment policy are obtained by solving HJB equations. We find that the optimal investment policy is affected by the correlation coefficient between the price of risky asset and price index.
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