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the binary outcome formulation you see everywhere is just "real" kelly boiled down. the real thing, which is contained fully in the first paragraph ("The Kelly
by sigstoat 6y ago
the binary outcome formulation you see everywhere is just "real" kelly boiled down. the real thing, which is contained fully in the first paragraph ("The Kelly bet size is found by maximizing the expected value of the logarithm of wealth"), has no such restrictions.
- fighterpilot 6y agoHow 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]