School of Mathematics, Shandong University

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.