  This paper is concerned with an optimal investment problem under correlated
noises in the financial market, and the expected utility functional is
hyperbolic absolute risk aversion (HARA) with the exponent $\gamma\neq0$. The
problem can be reformulated as a risk-sensitive stochastic control problem. A
new stochastic maximum principle is obtained first, where the adjoint equations
and maximum condition heavily depend on the risk-sensitive parameter and the
correlation coefficient. The optimal investment strategy is obtained explicitly
in a state feedback form via the solution to a certain Riccati equation, under
the risk-seeking case. Numerical simulation and figures are given to illustrate
the sensitivity for the optimal investment strategy, with respect to the
risk-sensitive parameter and the correlation coefficient.
