  The problem of portfolio optimization when stochastic factors drive returns
and volatilities has been studied in previous works by the authors. In
particular, they proposed asymptotic approximations for value functions and
optimal strategies in the regime where these factors are running on both slow
and fast timescales. However, the rigorous justification of the accuracy of
these approximations has been limited to power utilities and a single factor.
In this paper, we provide an accurate analysis for cases with general utility
functions and two timescale factors by constructing sub- and super-solutions to
the fully nonlinear problem so that their difference is at the desired level of
accuracy. This approach will be valuable in various related stochastic control
problems.
