 By employing the dual transform and smooth-fit principle,  the classical solution of the HJB equation is obtained in an analytical form, which in turn provides the feedback optimal investment and consumption .
<meaning-changed>  By employing the dual transform and smooth-fit principle,  the classical solution of the HJB equation is obtained in an analytical form, which in turn provides the feedback optimal investment and consumption .
 By employing the dual transform and smooth-fit principle, some thresholds of the wealth variable are derived such that the classical solution to the classical solution of the HJB equation is obtained in an analytical form, which in turn provides the feedback optimal investment and consumption .