Optimizing the growth rate of investment is considered a controversial
investment goal, perhaps because it is an asymptotic criterion or
perhaps because its implementation requires maximizing the expected
logarithm of wealth and its implicit suggestion of log utility. Whatever
the reason, we shall reverse the argument by focusing on the natural
mathematics of the solution rather than the appropriateness of the
question. Maybe graceful mathematics is an indication of the right approach.
We find that growth optimality is characterized by expected ratio
optimality, by competitive one-shot optimality, by Martingale processes
and an associated asymptotic equipartition theorem. It also yields Black
Scholes option pricing as a special case and leads naturally to so
called universal portfolios that perform as well to first order in the
exponent as the best constant rebalanced portfolio in hindsight.
Finally we will relate the quantities arising in investment to their
counterpart quantities in information theory.