Comment by fighterpilot

4 years ago

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

hahaha.

  • Right so just do a simulation, no closed form solution.

    • that's not simulation.

      for that trivial case, there's going to be a closed form solution. your nearest copy of mathematica can derive it for you.

      not that having a closed form solution is relevant to anything. the answer is still the answer.

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