Portfolio Risk Management with Entropy Based Importance Sampling

Abstract

Abstract

We provide an entropy-based importance sampling method to increase the accuracy for estimating default probabilities of some portfolios. The structure of these portfolios includes a summation of normal multivariate, a summation of student t multivariate, a mixture of normal variates and some student t variates , a summation of multi-dimensional geometric Brownian motions (basket of assets), and a summation of one dimensional geometric Brownian motion in different time (arithmetic sum in Asian option). The proposed entropy-based importance sampling method is a high-dimensional minimization problem of some relative entropy under some boundary constraint. It turns out this optimization problem is identical to some portfolio optimization problem under the classical mean-variance analysis. This relationship motivates a further study on computing the efficient frontiers of (1) portfolio consisting of multi-dimensional geometric Brownian motions and (2) portfolio as Asian weighted discrete time geometric Brownian motion.

Abstract

We provide an entropy-based importance sampling method to increase the accuracy for estimating default probabilities of some portfolios. The structure of these portfolios includes a summation of normal multivariate, a summation of student t multivariate, a mixture of normal variates and some student t variates , a summation of multi-dimensional geometric Brownian motions (basket of assets), and a summation of one dimensional geometric Brownian motion in different time (arithmetic sum in Asian option). The proposed entropy-based importance sampling method is a high-dimensional minimization problem of some relative entropy under some boundary constraint. It turns out this optimization problem is identical to some portfolio optimization problem under the classical mean-variance analysis. This relationship motivates a further study on computing the efficient frontiers of (1) portfolio consisting of multi-dimensional geometric Brownian motions and (2) portfolio as Asian weighted discrete time geometric Brownian motion.