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One kind of corporate optimal investment problem: Inflation case

This paper is concerned with one kind of corporate optimal portfolio problems in the inflation case. The investor can put her or his money either in the bank account or in a real project. We use a conjecture method, which can often be found when studying linear quadratic (LQ) optimal control problem, to give an explicit solution to our optimal problem in the special Constant Relative Risk Aversion (CRRA) case. We also give some simulation results to illustrates the influence of volatility parameters on the optimal investment strategy.