Optimization problems in the simulation of multifactor portfolio credit risk

Abstract

We consider some optimization problems arising in an efficient simulation method for the measurement of the tail of portfolio credit risk. When we apply an importance sampling (IS) technique, it is necessary to characterize the important regions. In this paper, we consider the computation of directions for the IS, which becomes hard in multifactor case. We show this problem is NP-hard. To overcome this difficulty, we transform the original problem to subset sum and quadratic optimization problems. We support numerically that these reformulation is computationally tractable.