Maximization of Consumption and Portfolio Problem under Interest Spreads of Deposit and Loan and Transaction Costs

摘要

Under the assumption that there exists transaction costs and interest spreads between deposit and loan in financial market, we investigate the maximization problem of consumption utility of an investor in his expected lifetime. The value function of the problem is derived in closed form, and optimal controls are obtained explicitly. Furthermore, we discuss the relationship between interest and consumption for different cases, meanwhile we give the relationship of wealth and consumption. Finally, we present the intuitive graphs for different cases.