[srinivgp]

It does not. It maximizes log-wealth. Maximizing expected wealth gives a strategy which results in $0 a lot of the time but much much more than Kelly occasionally, achieving a higher average wealth. Kelly gives that up, getting far less expectation of actual wealth, but far more expectation of log-wealth (which is -inf at $0 so avoids the $0 results). If you don't believe this, pick any one scenario and actually do the math, take the limits, etc.

[LudwigNagasena]

> It does not. It maximizes log-wealth. Maximizing expected wealth gives a strategy which results in $0 a lot of the time but much much more than Kelly occasionally, achieving a higher average wealth.

Log utility function is u(w) = log(w), that’s what it is called in economics. Surely maximizing log of wealth means you are maximizing log utility function.

> Kelly gives that up, getting far less expectation of actual wealth, but far more expectation of log-wealth (which is -inf at $0 so avoids the $0 results).

That’s a crucial misunderstanding of the Kelly’s result. He doesn’t give anything up. He showed than in a nonterminating game the strategy of betting as if you have log utility will give you superior results to any other strategy in terms of long-term wealth growth. What if the game is terminating? Well, in that case you need to know the utility function of the gambler to determine a superior strategy. But in a non-terminating game it is a bit irrelevant because almost all strategies will lead to infinite utility.

[eru]

(If memory serves right), for bets that either win or double, the Kelly criterion is equivalent to maximize the median wins. Which coincidentally also maximizes expected log wins.

[kqr]

That's an interesting connection! I've heard risk managers talk about how people put too much faith in the mean outcome and don't focus enough on the median outcome. I didn't know there's a correspondence to the Kelly criterion.

[eru]

See also https://www.stat.berkeley.edu/~aldous/157/Papers/Good_Bad_Ke...