Moment Matching

We examine the stability of a portfolio management model based on the conditional value-at-risk (CVaR) measure. The stochastic programming model controls total risk exposure of an international investment portfolio. This includes both market risk in multiple countries as well as currency exchange risk. Uncertainty in asset returns and exchange rates is modeled in terms of discrete scenarios that are generated by means of a moment matching method. The procedure generates a set of scenarios with statistical properties of the random variables matching specific target values that are estimated using historical market data. First, we establish that the scenario generation procedure does not bias the results of the optimization program, and we determine the required number of scenarios to attain stable solutions. We then investigate the sensitivity of the CVaR model to errors (mis-specifications) in the statistics of stochastic parameters (i.e., mean, variance, skewness and kurtosis of th...

The calculation of the coupled response of a structure with an enclosed acoustic cavity is of great interest, with many practical applications in the automotive and aerospace industries. Tra- ditional methods such as a fully coupled fluid-structure interaction finite element calculation can be very computationally expensive, and methods have been proposed that reduce this computa- tional burden and make it

In this paper, the well-known problem of finding a suitable interpolation point in order reduction via moment matching by Krylov subspaces is investigated. By using the equivalence property of moment matching and Laguerre-based order reduction, the problem is reformulated as finding the best choice for the free parameter ¿ in the Laguerre basis. Minimizing appropriate cost functions with very few iterations is the key point toward finding this best interpolation point.

During the past decade, Model Order Reduction (MOR) has become key enabler for the efficient simulation of large circuit models. MOR techniques based on momentmatching are well established due to their simplicity and computational performance in the reduction process. However, momentmatching methods based on the ordinary Krylov subspace are usually inadequate to accurately approximate the original circuit behavior. In this paper, we present a moment-matching method which is based on the extended Krylov subspace and exploits the superposition property in order to deal with many terminals. The proposed method can handle large-scale regular and singular circuits and generate accurate and efficient reduced-order models for circuit simulation. Experimental results on industrial IBM power grids demonstrate that our method achieves an error reduction up to 83.69% over a standard Krylov subspace method.

A reduced order model is developed for low frequency, undamped, fully coupled structural–acoustic analysis of interior cavities backed by flexible structural systems. The reduced order model is obtained by applying a projection of the coupled system matrices, from a higher dimensional to a lower dimensional subspace, whilst preserving essential properties of the coupled system. The basis vectors for projection are computed efficiently using the Arnoldi algorithm, which generates an orthogonal basis for the Krylov Subspace containing moments of the original system. The key idea of constructing a reduced order model via Krylov Subspaces is to remove the uncontrollable, unobservable and weakly controllable, observable parts without affecting the transfer function of the coupled system. Three computational test cases are analyzed, and the computational gains and the accuracy compared with the direct inversion method in ANSYS.It is shown that the reduced order model decreases the simulat...

In stochastic programming models we always face the problem of how to represent the random variables. This is particularly difficult with multidimensional distributions. We present an algorithm that produces a discrete joint distribution consistent with specified values of the first four marginal moments and correlations. The joint distribution is constructed by decomposing the multivariate problem into univariate ones, and using an iterative procedure that combines simulation, Cholesky decomposition and various transformations to achieve ...