Posted by
ML-21 on
Sep 08, 2004; 2:34am
URL: http://quantlib.414.s1.nabble.com/random-generation-of-constrained-portfolio-allocation-weights-tp3309p3316.html
> thank you for the setting the problem and for the paper.
Actually, I made a little mistake: I incorrectly wrote there were 2N+1
inequalities, but of course there are 2 inequalities and 1 equation.
However, that doesn't make a difference to the fundamental problem of having
to generate uniformly distributed variates on/in a multidimensional
polytope.
> >If there is interest, I'm happy to work on this issue and eventually
> >contribute a good algorithm.
> I am very interested! Please go ahead, and let me know how can I help you.
I wrote a short (and unverified!) program that lists the vertices of the
polytope (
http://luoni.net/junk.Rs9qq8xWa/rng.tar.gz). Generally speaking,
the number of vertices grows with N!, so the polytope becomes quickly very
complex. However, my guess/hope is that there will be a feasible solution
thanks to the simplicity of the underlying (in)equalities.
I am wondering whether the limits for the individual positions of the
portfolio are necessarily identical?
> > For the time being, however, I guess the rejection method is a
> > moderately good solution.
> Hmmm... what do you mean exactly?
Due to my mistake mentioned above I think I have to withdraw that statement
:-)
-Mario