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Comment by sigstoat

4 years 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.

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sigstoat

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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.

  • sigstoat  4 years ago

    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.