The corporate optimal portfolio and consumption choice problem in the real project with borrowing rate higher than deposit rate

In this paper, one kind of corporate optimal portfolio and consumption choice problem is studied for a investor who can invest his wealth in the bond (bank account) and in a real project which has the production. The bank pays at an interest rate for any deposit and takes at a large rate for any loan. The optimal strategies are obtained by Hamilton–Jacobi–Bellman equation which is derived from dynamic programming principle. We also give the economic analysis to the optimal choice using the investment theory. For the specific Hyperbolic Absolute Risk Aversion case, we get the explicit optimal investment and consumption solution. At last, we give some simulation results to illustrate the optimal result and the influence of the volatility parameter on the optimal choice.