The Kelly formula is meant to be a simple test to determine the optimal leverage (capital allocation) for multiple strategies. Investopedia has a page on it too. I hope that gets you pointed in the right direction, I plan to incorporate the Kelly formula into an algo when I get the time, I'll be sure to post it.

my framework https://github.com/Novaleaf/QuantShim is focused on providing multiple strategies to control their own positions. If you want an example of portfolio selection for mean revision, try looking here: https://www.quantopian.com/posts/collab-request-on-robust-median-reversion-strategy

otherwise, what David says about the Kelly formula seems applicable.

I am afraid Kelly formula does not provide more insights than the mean-variance paradigm.

I checked the paper cited in Wikipedia for multiple instruments: Nekrasov, Vasily(2013).
But I found the solution is nothing more than mean-variance theory.

The authors utilize Taylor expansion to approximate the Kelly problem to second order, which is almost the mean-variance optimization problem.
The numeric solution of full Kelly formula (no approximation) in that study also shows it is very close to the closed solution in Merton(1969), which is, again, mean variance theory.

Thus, most issues on mean-variance theory (e.g. noise of estimation for mean and variance) applies here.
I have not search all the literature on Kelly formula. But most papers cited in Nekrasov, Vasily(2013) seem partial.

The example of portfolio selection for mean revision looks nice although it may work only for mean reversion!

I would love to know if there is any idea like this that approaches from other perspective.
Many thanks.

The Ernie Chan book from 2007 describes how to use the Kelly to do allocation. Probably his newer one from 2012 does too. I only skimmed it over because I'm rusty with math, and I'd need at least two useful strategies/portfolios before worrying about that... which I do not :P

Thanks for Jason's suggestion. But the answer is probably the same as mean-variance theory.
The book by Ernest Chan I have referred to is "Algorithmic Trading" (2013). I surmise the other books are the same.

The formula (8.2) on page 173 is F=C^-1 * M,
F for the weight of each instrument and C for the covariance matrix and M for the mean excess return.

This is exactly the solution from Markowitz's portfolio theory or equation (60) in Merton (1969) :http://www.lifecycleinvesting.net/Resources/merton%20lifetime%20portfolio%20selection%201969.pdf.

I surmise most solutions based on the first two moments of return distribution (namely, approximate by normal distribution) will lead to the same answer as mean-variance theory.

To deviate from the result, one must approach from non-parametric or more general perspective such as robust-median-reversion-strategy mentioned above.
It seems this question still remains quite open.

Hi Eric
first of all many thanks for your interest to my paper

I am afraid Kelly formula does not provide more insights than the mean-variance paradigm.
I checked the paper cited in Wikipedia for multiple instruments: Nekrasov, Vasily(2013).
But I found the solution is nothing more than mean-variance theory.

Well, numerically Kelly delivers very similar results to Markowitz (unless the return tails are too heavy).
But conceptually they are very different (have a look at this interesting note http://www.decal.org/file/1071)
Moreover, formally my approach is not mean-variance (mean yes, but instead of variance I consider the matrix of second non-centralized moments).

Thus, most issues on mean-variance theory (e.g. noise of estimation for mean and variance) applies here.

Unfortunately this is true (and I mention it in the current version of my paper).
But Kelly is not a "do as I said" approach. Rather it is a powerful tool to estimate what you can get at best from your trades in the long term.
In my book (http://www.yetanotherquant.com) I provide some insights how to apply Kelly criterion for practical portfolio construction.