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Metus comments on How much to spend on a high-variance option? - Less Wrong Discussion
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I am trying to understand the implications of the kelly criterion for a real world portfolio. What I get as a result is that if I have free choice on any bet at any odds and chances I should, in total, invest more than I have. (Result by integrating over all probabilities/odds that allow positive expected value) In fact, I should invest infinitely much money. The wikipedia page states that taking out credit to buy a bet would be formalized by the loss formula so the infinity result is not exactly interpretable as taking out a loan, if I can.
One obvious fix is to limit the odds and probabilites to realistic values but that seems quite arbitrary. Intuitively I would expect the Kelly criterion to give a finite sum for all bets with positive expected value, at least it does so for any given odds b in wikipedias terminology.
If you invoke infinities or indefinite sets of bets, it shouldn't surprise you that regular results might not apply: if you decide to invest in a bet of n at 99% odds of doubling, wouldn't it be even better to invest n at 99% odds of tripling? Or even better than that, invest n at 99.9% odds of tripling? Or no, invest n+1 at 99.9% odds of tripling! I'm not sure why you'd expect anything useful from a KC or a variant with such arbitrary inputs.
It does?
You are right.
It does seem arbitrary because for sufficiently high intervals for p and b the integral will exceed 1, that is allocation of all my cash and I do not know how to interpret this result.