Maximum principle for a stochastic optimal control problem and application to portfolio/consumption choice

We consider mainly an optimal control problem motivated by a portfolio and consumption choice problem in a financial market where the utility of the investor is assumed to have a given homogeneous form. A Pontryagin local maximum principle is obtained by using classical variational methods. We apply the result to make optimal portfolio and consumption decisions for the problem under consideration. The optimal selection coincides with the one obtained in earlier papers, where Bellman dynamic programming principle was used.