Capital Allocation On Simultaneously Arriving Signals in the Same Direction but....

[Nonius]

I think Kelly would dictate something like this. tell me what you think?

[url=/User%20Files/14/photo.pdf]Attached File: photo.pdf[/url]

[benji]

this is correct (except on page two line one you forgot to carry over [img]/User%20Files/492/Latex-Equation-11287.gif[/img]) solving for this equals to zero is standard kelly.

[SimJimons]

Betting full Kelly is a perfectly safe way to disaster, unless you know your odds exactly! Betting fractional Kelly is simply the same as allocating according to signal strength, with a margin of safety, while rebalancing continuously. Isn't it? Anyway, I would treat each signal separately or, if that is not possible due to size, according to combined signal strength. When I read my answer I get the feeling that I'm not really understanding what you are asking for Smiley

[Nonius]

well, funny you say signal strength, i was thingking that the r term in the thorp paper really should represent a hurdle rate below which your fraction is basically zero.

[Nonius]

by the way Benji, thanks for noting the stupid carry over error.



now, absent constraints, given a certain level of degeneracy, the solution space is clearly going to look like the inversion of a hyperspace, ie, the solution is going to be solving a system:



Av=B where the components of B are parameterized by 1/f(u) f being a linear functional and A is a matrix and v is the final solution.



having said that, our bet sizes are postive in value, hence we have the constraint that each y>=0. before solving this, wouldn't you think that the solution is going to be "on the boundary" ie, the best trade is going to be choose the one stop gain and stop loss that has the highest expected log return and ignore the others?



by the way, I note that at least three people have requested..."Algorithms for optimal allocation of bets on many simultaneous events" in the paper request thread...that's basically the problem.



edit: ok, with the constraints it's a pretty standard convex optimization problem.

[frstwrldprblm]

thanks for this post. the papers listed are great and pointed out some people doing very interesting research.

[Nonius]

well, i coded up the paper i cited below. works but its the wrong problem, as he assumes a constraint of investing 100 pc of wealth. coded up a home grown version that looks promising. i convert into an unconstrained problem by first mapping each coordinate to 1/(1+exp(-t)), which maps the line to the unit open interval. then, i map the unit cube to the simplex (all variables nonegative and sum to less than or equal to one) using the usual inductive trick....may aks for a volunteer to check the code but prelimnary tests are promising.

[ricko]

This is an interesting problem encountered often when using price patterns as components of trading systems, like the ones generated by the program Michael Harris has developed. Besides simultaneity there is also the possibility of overlappings which one should handle properly to gain maximum expectancy. Instead of repeating here what Michael Harris suggests here is a link to his classification.. I think the problem of simultaneous signals is much easier as one could allocate based on the proportion of their probabilities and possibly weighted by the stop-loss. It is interesting to see that overlaping signals if treated properly can emulate trend-following by suitably moving the stop-loss and stop-gain while re-affirming probability of win.



A mathematical treatment of this would be interesting imo.

[quantz]

Interesting thread/paper. Had not considered the problem from this perspective before.