Before revision:  We obtain the closed-form optimal wealth with an ES constraint as well as with a VaR constraint respectively, and explicitly calculate the optimal trading strategy for a CRRA (i.e., constant relative risk aversion ) utility function .
After revision:  We obtain the closed-form optimal wealth with an ES constraint as well as with a VaR constraint respectively, and explicitly calculate the optimal trading strategy for a CRRA (i.e., constant relative risk aversion (CRRA) utility functions .