In this talk we discuss a continuous time optimization problem which combines two conflicting objectives of  maximizing the portfolio wealth up to a level and minimizing  the conditional value-at-risk of the portfolio wealth loss. The standard utility maximization theory cannot be applied to solve the problem as the associated utility function is not differentiable nor strictly concave and does not satisfy Inada's condition. We use the dual control method to show that there is a classical solution to the Hamilton-Jacobi-Bellman equation and that the optimal value function is  smooth  if the optimal control satisfies an exponential moment condition. In the special case of wealth maximization we find the closed-form optimal feedback control and  optimal value function.