[brettd]

Assuming I had bankroll, of which x% was leveraged, how would the use of the Kelly Criterion be affected? Or does Kelly not apply in this instance?

I suppose other considerations would be the interest the leverage would incur.

Assuming a leveraged bankroll and assuming a 'leverage adjusted kelly', what would be the best course of action in paying off the leverage?

My mathematical ability goes way beyond trying to answer this one.

Hey Ganchrow (or anyone with Ganchrow-like mathematical ability), got any ideas here?

[Ganchrow]

Kelly assumes constant relative risk aversion irrespective of relative size of bankroll.

For Kelly multipliers ≤ the loss of an entire bankroll would necessarily be infinitely "bad".

Because of this Kelly won't work "out-of-the-box" with any reasonable assumption of leverage.

[Data]

When it comes to financial markets and you are, say, a hedge fund, your bankroll does not change and you use the leverage to invest more than your total bankroll if Kelly calls for that. I cannot imagine how leverage should/would work in sports betting. However, for a gambler, all the money you can borrow are part of your Kelly bankroll.

[brettd]

Because of this Kelly won't work "out-of-the-box" with any reasonable assumption of leverage.

So what sort of modifications need to take place? Is this some serious maths? What would you recommend in its place, given a situation like this?

[MonkeyF0cker]

Instead of looking for a variant of Kelly, perhaps what you could look to do is to create a utility function (perhaps some sort of time-constrained Markov Chain MCML model) that recalculates your effective bankroll based on an optimal amount (or percentage of a static amount) of leverage added to your bankroll. Obviously, this is a non-ergodistic solution and you would need to employ some sort of personal metric for risk aversion.

[MonkeyF0cker]

Optimally, however, apart from individual utility, the leveraged portion of your bankroll would be no different than the rest of your bankroll in terms of Kelly.

[MarketMaker]

I think it would be important to know if this leverage amount is actual cash borrowed or credit granted.

If it is actual cash, and the cash will remain available indefinitely, then you should consider the entire amount your bankroll and use kelly accordingly.

If this leverage is simply credit granted then you should not consider it in your bankroll and should calculate kelly based on a bankroll of actual cash available.