How do you maximize the E(log(wealth)) when applied to a HFT strategy? In such a strategy we have N sequential bets, each bet has a roughly normal distribution outcome with mean just above zero.
The example on Wikipedia supposes we are investing in a geometric Brownian motion and a risk free asset.
in the U(-1.0, 1.1) case you mentioned, kelly says not to bet.
optimize the value of the bet size over the expected value of the log of bankroll + betsize*outcome. you can do that for any probability distribution of outcomes.
if you can't write that in 5 minutes, then i already did half your homework for you.
> each bet has a roughly normal distribution outcome
The example on Wikipedia supposes we are investing in a geometric Brownian motion and a risk free asset.