Andrew...A solution is readily calculated from the general (non-constrained
to sigma 1) solution. The actual solution is a manifold of points. However
one of those points within that manifold is a simple, linear solution
between the fractions 0,0..0 and k,k....k the latter being the loci of the
(asymptotic! i.e. as the number of holding periods approach infinity) peak
(what you call the Kelly-Criterion solution, a calculation that, as used in
capital markets, is often not adjusted properly and a source of danger.
This is alluded to in the introduction of
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2364092).

So to find a point on the manifold of asymptotic, expected growth-optimal
points, one can start with the solution that is the asymptotic expected
growth-optimal peak, then that point with the same relative weightings but
where the sigma of the weights <=1 is on that manifold.


-Ralph Vince


On Wed, Jan 22, 2014 at 5:33 AM, Andrew O <andrewoskoui@gmail.com> wrote:

> I'm trying to do a kelly criterion optimization of a group of simultaneous
> binary bets.  Each bet has two values associated with it, the probability
> of
> success, P, and the payout if successful, r.  If the bet loses, the entire
> premium is lost.
>
> So if I put in a set of 20 bets that need to be bet on simultaneously, what
> is the ideal weighting, X, to give to each to maximize the growth of
> capital
> from placing those bets.  This is obviously more difficult than the trivial
> calculation of figuring out the highest expected value(all capital invested
> in the bet with the most profitable bet).
>
> A paper, "Algorithms for optimal allocation of bets on many
> simultaneous events", gives a more detailed description of the problem
> here:
> http://www.filedropper.com/whitrow2007kellypaper
>
> For me, the limitations on the calculation are that all values for X must
> be
> positive (long only) and the sum of all the X must be less than or equal to
> 1 (no leverage).
>
> Are there any packages or methods that would be useful for solving this
> kind
> of problem?
>
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