  The focal point of this paper is the so-called Kelly Criterion, a
prescription for optimal resource allocation among a set of gambles which are
repeated over time. The criterion calls for maximization of the expected value
of the logarithmic growth of wealth. While significant literature exists
providing the rationale for such an optimization, this paper concentrates on
the limitations of the Kelly-based theory. To this end, we fill a void in
published results by providing specific examples quantifying what difficulties
are encountered when Taylor-style approximations are used and when wealth
drawdowns are considered. For the case of drawdown, we describe some research
directions which we feel are promising for improvement of the theory.
