  In this paper, we consider a discrete-time portfolio with $m \geq 2$ assets
optimization problem which includes the rebalancing~frequency as an additional
parameter in the maximization. The so-called Kelly Criterion is used as the
performance metric; i.e., maximizing the expected logarithmic growth of a
trader's account, and the portfolio obtained is called the frequency-based
Kelly optimal portfolio. The focal point of this paper is to extend upon the
results of our previous work to obtain various optimality characterizations on
the portfolio. To be more specific, using Kelly's criterion in our
frequency-based formulation, we first prove necessary and sufficient conditions
for the frequency-based Kelly optimal portfolio. With the aid of these
conditions, we then show several new optimality characterizations such as
expected ratio optimality and asymptotic relative optimality, and a result
which we call the Extended Dominant Asset Theorem. That is, we prove that the
$i$th asset is dominant in the portfolio if and only if the Kelly optimal
portfolio consists of that asset only. The word "extended" on the theorem comes
from the fact that it was only a sufficiency result that was proved in our
previous work. Hence, in this paper, we improve it to involve a proof of the
necessity part. In addition, the trader's survivability issue (no bankruptcy
consideration) is also studied in detail in our frequency-based trading
framework. Finally, to bridge the theory and practice, we propose a simple
trading algorithm using the notion called dominant asset condition to decide
when should one triggers a trade. The corresponding trading performance using
historical price data is reported as supporting evidence.
