Financial portfolio optimisation

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. 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.