A class of log-optimal utility functions

One of the classic observations in investment theory is that maximizing the expected-log-return of a portfolio results in the greatest long-term growth of wealth. The log-optimal portfolio is both competitively optimal and pathwise dominant. Nevertheless, investment researchers and practitioners don't all latch on to the log-optimal doctrine, even for theoretical guidance. A common alternative is to use a utility function to evaluate an investment strategy. At first glance it seems that any (non-decreasing) utility function would point to the log-optimal portfolio, at least in the limit. This is known not to be the case. In this work we identify sufficient conditions on a utility function that will produce a happy marriage between utility theory and optimal growth-rate of wealth.