Optimal investment consumption model with a higher interest rate for borrowing

This paper considers a consumption and investment decision problem with a higher interest rate for borrowing as well as the dividend rate.Wealth is divided into a riskless asset and risky asset with logrithmic Brownian motion price fluctuations.The stochastic control problem of maximizating expected utility from terminal wealth and consumption is studied.Equivalent conditions for optimality are obtained.By using duality methods,the existence of optimal portfolio consumption is proved,and the explicit solutions leading to feedback formulae are derived for deteministic coefficients.