  In this paper, I'll derive the Hamilton-Jacobi (HJ) equation for Merton's
problem in Utility Optimization Theory using a Calculus of Variations (CoV)
Approach. For stochastic control problems, Dynamic Programming (DP) has been
used as a standard method. To the best of my knowledge, no one has used CoV for
this problem. In addition, while the DP approach cannot guarantee that the
optimum satisfies the HJ equation, the CoV approach does.
  Be aware that this is the first draft of this paper and many flaws might be
introduced.
