  We study the continuous time portfolio optimization model on the market where
the mean returns of individual securities or asset categories are linearly
dependent on underlying economic factors. We introduce the functional
$Q_\gamma$ featuring the expected earnings yield of portfolio minus a penalty
term proportional with a coefficient $\gamma$ to the variance when we keep the
value of the factor levels fixed. The coefficient $\gamma$ plays the role of a
risk-aversion parameter. We find the optimal trading positions that can be
obtained as the solution to a maximization problem for $Q_\gamma$ at any moment
of time. The single-factor case is analyzed in more details. We present a
simple asset allocation example featuring an interest rate which affects a
stock index and also serves as a second investment opportunity. We consider two
possibilities: the interest rate for the bank account is governed by
Vasicek-type and Cox-Ingersoll-Ross dynamics, respectively. Then we compare our
results with the theory of Bielecki and Pliska where the authors employ the
methods of the risk-sensitive control theory thereby using an infinite horizon
objective featuring the long run expected growth rate, the asymptotic variance,
and a risk-aversion parameter similar to $\gamma$.
