The Corporate Optimal Portfolio and Consumption Choice Problem in Trade Project with Borrowing Rate Higher than Deposit Rate

This paper is concerned with a kind of optimal portfolio and consumption choice problem, where an investor can invest his wealth in a trade project and foreign exchange deposit. The trade project earns profit by buying the merchandise and selling it with a higher price. The bank pays at an interest rate for any deposit, and vice takes at a large rate for any loan. The optimal strategy is obtained by Hamilton-Jacobi-Bellman (HJB) equation, which is derived from dynamic programming principle. For the specific Hyperbolic Absolute Risk Aversion (HARA) case, we get the explicit form of optimal portfolio and consumption solution, and we give some simulation results.