Financial Portfolio Optimization

         Pierre Flener (pierref@it.uu.se), Justin Pearson
               Department of Information Technology
                    Uppsala University, Sweden

                          Luis G. Reyna
             Global Private Investment Advisory Group,
                   Merrill Lynch, New York, USA

Abstract:
We give an approximate and often extremely fast method of solving a
portfolio optimisation (PO) problem in financial mathematics, which
has applications in the credit derivatives market (synthetic CDO,
CDO^2, CDO squared, Russian-doll CDO, ...).  Its corresponding
satisfaction problem is closely related to the balanced incomplete
block design (BIBD) problem.  However, typical PO instances are an
order of magnitude larger than the largest BIBDs solved so far by
global search.  Our method is based on embedding sub-instances into
the original instance.  Their determination is itself a CSP.  This
allows us to solve a typical PO instance, with over 10^746 symmetries.
The high quality of our approximate solutions can be assessed by
comparison with a tight lower bound on the cost.  Also, our solutions
sufficiently improve the currently best ones so as to often make the
difference between having or not having a feasible transaction due to
investor and rating-agency constraints.

Paper published in:
M. Wallace (editor), Proceedings of CP'04, the 10th International Conference
on Principles and Practice of Constraint Programming, pp. 227-241.
Lecture Notes in Computer Science, volume 3258.  Springer-Verlag, 2004.
(http://www.springerlink.com/index/7RGRUR32BVCML16T)