Kelly Criterion for an example

There's a 55% chance of winning, 45% chance of losing. 

A win will result in 35% increase (e.g. $100->$135). A loss will result in a 30% loss ($100->$70). 

What's the Kelly Criterion? (please show work)

Math Finance
Dforootan Dforootan
24
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Kav10 Kav10
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  • Dforootan Dforootan
    0

    Thanks. What's been confounding me is the partial loss here. It seems b is a bet ratio, and partials aren't covered in this version of the formula?

    • Kav10 Kav10
      0

      Win gains 35% and lose loss is 30%. There is no partial loss. See both formulas, they calculate it using two separate approaches.

  • Dforootan Dforootan
    0

    The formula I looking at was f* = [bp − aq] / ab , difference is denominator is multiple loss and gain, that's not accurate?

    • Kav10 Kav10
      0

      No. That’s not!

  • Dforootan Dforootan
    0

    @kav10 i'm going to accept this because the prize is too low. I want to open another question (or I'm happy to tip $50 here) to dig further into this because I've only been able to make all derivatives get the same values if there is a total loss, not a partial loss. You can see https://streetfins.com/the-kelly-criterion-explained/ and https://en.wikipedia.org/wiki/Kelly_criterion (under Investing Formula) f* = [bp − aq] / ab = p/a - q/b and f=(bp-q)/b match when there is a total loss of a

    • Kav10 Kav10
      0

      Looks like you have not accepted yet! I’ve already solved the question with two approaches and answered your questions all for $4. Do you think that’s fair?

    • Kav10 Kav10
      0

      Please state specifically what you need for the additional money. It should take me less than hour as my rate is $60/hour. Or you can just open a new question.

  • Dforootan Dforootan
    0

    Also can see Thorp's page 7, lines 25-28: https://wayback.archive-it.org/all/20090320125959/http://www.edwardothorp.com/sitebuildercontent/sitebuilderfiles/KellyCriterion2007.pdf "One claim was that one can only lose the amount bet so there was no reason to consider the (simple) generalization of this formula to the situation where a unit wager wins b with probability p > 0 and loses a with probability q. Then if the expectation m ≡ bp − aq > 0, f∗ > 0 and f∗ = m/ab."

    • Kav10 Kav10
      0

      Remember that there are two main versions of the Kelly Critereon formula, one used for Gambling and one used for Investment. Regarding your question about partial loss, I did some research and a more general form of Kelly's formula considers the partial loss associated with an investment: {\displaystyle f^{*}={\frac {p}{a}}-{\frac {q}{b}}}

    • Dforootan Dforootan
      -1

      This is not correct. See https://matchmaticians.com/questions/npszwx

  • Dforootan Dforootan
    0

    This = The answer*

    • Dforootan Dforootan
      0

      Per my other question: the correct formula is {\displaystyle f^{*}={\frac {p}{a}}-{\frac {q}{b}}}, where a and b 0

    • Dforootan Dforootan
      0

      comment got cut off … a and b are between 0 and 1. The first formula above in the answer is just the case where a=1 the second formula above in the answer seems to just not work.

The answer is accepted.
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