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That’s wrong. The assumptions behind the Kelly criterion lead to the log utility only in a particular case. What if each week you can bet $1 that in 50% of cas
by LudwigNagasena 5y ago
That’s wrong. The assumptions behind the Kelly criterion lead to the log utility only in a particular case.
What if each week you can bet $1 that in 50% of cases will triple your bet and in 50% of cases will give you $0? According to the log utility whether you should bet depends on your current wealth. According to the assumptions behind the Kelly criterion you should take the bet every week.
- kqr 5y agoTechnically the Kelly criterion suggests you should take this bet if your wealth is greater than $1.23, so it does depend on your current wealth. However, this might still look dumb, and it's because my calculation assumes you could pick a smaller stake for the same bet, which isn't necessarily the case. If you can't, the calculation gets a little bit more complicated, but sure, the Kelly criterion can deal with that too.
- LudwigNagasena 5y agoAccording to the assumptions behind the Kelly criterion (maximizing long-term growth rate) you should always take the bet. Kelly criterion can’t be applied here because we have a different setup (you can’t choose your bet size), that’s my entire point!