Stochastic optimal control for investment-consumption model with quadratic transaction costs

In this paper, a stochastic optimal control problem is formulated and solved for an investment and consumption model that includes stocks and bonds with transactions costs. In contrast to earlier results which considered linear transaction rate and got a non-singular feedback controls, we propose to use a quadratic transaction rate function to take into account of the liquidity of the bond and stock. The Taylor expansion is utilized to obtain an important initial condition in order to solve the nonlinear differential HJB equation numerically. The simulation studies are also carried out to quantify the effect of the transactions costs on the optimal investment-consumption policies.