This paper studies a type of periodic utility maximization for portfolio
management in an incomplete market model, where the underlying price diffusion
process depends on some external stochastic factors. The portfolio performance
is periodically evaluated on the relative ratio of two adjacent wealth levels
over an infinite horizon. For both power and logarithmic utilities, we
formulate the auxiliary one-period optimization problems with modified utility
functions, for which we develop the martingale duality approach to establish
the existence of the optimal portfolio processes and the dual minimizers can be
identified as the "least favorable" completion of the market. With the help of
the duality results in the auxiliary problems and some fixed point arguments,
we further derive and verify the optimal portfolio processes in a periodic
manner for the original periodic evaluation problems over an infinite horizon.Comment: 28 pages, 33 conferenc