VNS approach for solving a financial portfolio design problem

Abstract

This paper introduces a VNS based local search for solving efficiently a financial portfolio design problem which affects assets to portfolios, subject to a compromise between maximizing gains and minimizing losses. This practical problem appears in financial engineering, such as in the design of CDO-squared portfolios. This problem has been modeled by Flener et al. who proposed an exact method to solve it. We propose a matricial model showing that the problem can be formulated as a quadratic program on the 0-1 domain. It is well known that exact solving approaches on large instances of quadratic integer programs are known to be costly. Thus it is a challenging problem for local search methods which have not been already investigated. The matricial 0-1 model of the problem enables to specialize VNS algorithm by taking into account the particular structure of the considered financial problem. First experimentations show that VNS with simulated annealing is effective on non-trivial instances of the problem.