2 ms·
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
by fighterpilot 6y 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.
- sigstoat 6y agoin 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.
- fighterpilot 6y agoRight so just do a simulation, no closed form solution.
- sigstoat 6y agothat'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.
- deleted 6y ago[deleted]