Timeline for Intuition for why Kelly criterion is 'so simple'
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Jun 24 at 12:55 | comment | added | Henry | "higher wealth than any other strategy in the long run (i.e., the theoretical maximum return as the number of bets goes to infinity)" is not tightly defined. Assuming the available bets have a positive expected value, there are many other strategies which have an infinite expected return as the number of bets goes to infinity. Some of these strategies give a higher expected return for any finite number of bets though with a risk of a high probability of substantially lower returns too. So you need more to get the Kelly result, essentially equivalent to logarithmic utility. | |
| Jun 22 at 14:45 | history | edited | LSpice | CC BY-SA 4.0 |
Proofreading
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| Jun 22 at 14:16 | comment | added | wood | Thanks, the scaling argument is convincing. It depends on the fact that we can scale arbitrarily, which is somehow implicit in the formulation of the Kelly criterion. | |
| Jun 22 at 14:08 | history | edited | wood | CC BY-SA 4.0 |
added 1487 characters in body
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| Jun 21 at 3:31 | comment | added | Timothy Chow | I agree with Martin M. W. Asking for a convincing heuristic argument is a bit delicate. If the argument were totally convincing, then it wouldn't be a heuristic; it would be a rigorous proof. So no matter what heuristic argument is proposed, one can fault it for being not totally convincing. But certainly, if it's optimal to bet 200 dollars when you have 1000 dollars, then it is intuitive that it's optimal to bet 2 dollars when you have 10 dollars. After all, if it's optimal to bet 200 dollars with 1000 dollars then it's surely optimal to bet 200 cents with 1000 cents. | |
| Jun 20 at 12:10 | comment | added | Martin M. W. | For #2, it makes sense the criterion would be scale linearly: it shouldn't matter whether you count your money in dollars or yen. For #1, one way to think of the Kelly strategy is maximizing time diversification—and anything other than a single fixed percentage would be weighting some bets more than others. However, intuition only takes you so far. An actual rigorous proof is kind of messy! | |
| Jun 20 at 12:09 | comment | added | Nate River | @PeterLeFanuLumsdaine Ah, fair enough. | |
| Jun 20 at 11:59 | comment | added | Peter LeFanu Lumsdaine | That Wikipedia article cites various serious-looking sources (published articles in maths and economics) for the arguments/claims you’re asking about. Have you followed up those citations? They may answer your doubts, or (if they turn out to be equally unsatisfying) you can improve the question by pinpointing your issues more precisely. @NateRiver: I guess that’s the reason this question is downvoted: it complains that arguments in a Wikipedia article are vague/imprecise, but shows no evidence of having followed back to the citations, which is the obvious first thing to try. | |
| Jun 20 at 9:47 | comment | added | Nate River | I do not know why this is downvoted and voted to close, it is a good question... | |
| Jun 19 at 20:41 | review | Close votes | |||
| Jun 24 at 3:08 | |||||
| Jun 19 at 20:11 | history | asked | wood | CC BY-SA 4.0 |