A Stochastic Maximum Principle for Optimal Control of Jump Diffusions and Applications to Finance

An optimal control problem motivated by a portfolio and consumption choice problem in the financial market where the expected utility of the investor is assumed to be the Constant Relative Risk Aversion (CRRA) case is discussed. A local stochastic maximum principle is obtained in the jump-diffusion setting using classical variational method. The result is applied to make optimal portfolio and consumption choice strategy for the problem and the explicit optimal solution in the state feedback form is given.