Global Optimization of the Scenario Generation and Portfolio Selection Problems

We consider the global optimization of two problems arising from financial applications. The first problem originates from the portfolio selection problem when high-order moments are taken into account. The second issue we address is the problem of scenario generation. Both problems are non-convex, large-scale, and highly relevant in financial engineering. For the two problems we consider, we apply a new stochastic global optimization algorithm that has been developed specifically for this class of problems. The algorithm is an extension to the constrained case of the so called diffusion algorithm. We discuss how a financial planning model (of realistic size) can be solved to global optimality using a stochastic algorithm. Initial numerical results are given that show the feasibility of the proposed approach.