INDUSTRIAL ENGINEERING AND
OPERATIONS RESEARCH
PRESENTS
IEOR SEMINAR
Monday
Title: Tools for higher order portfolio optimization
Speaker: Jason Morton, Dept of Math., Stanford University
Abstract
Gaussian data is completely characterized by its mean and covariance. However modern data are almost always non-Gaussian and higher-order statistics such as cumulants are inevitable. For univariate data, the third and fourth cumulants are scalar-valued and relatively well-studied as skewness and kurtosis. But for multivariate data, these cumulants are tensor-valued, higher-order analogs of the covariance matrix capturing higher-order dependence in the data. In addition to their relative obscurity, there are few effective methods for analyzing these cumulant tensors. We propose a technique along the lines of Principal Component Analysis and Independent Component Analysis to analyze multivariate, non-Gaussian data motivated by the multilinear algebraic properties of cumulants. Our method relies on finding the principal cumulant components that account for most of the variation in all higher-order cumulants, in the same manner PCA obtains varimax components for Gaussian data. An efficient algorithm based on limited-memory quasi-Newton maximization over a Grassmannian, using only standard matrix operations, may be used to find the principal cumulant components. Applications include multi-moment portfolio optimization and image dimension reduction.
TIME AND LOCATION:
COME EARLY REFRESHMENTS WILL BE SERVED AT 3:00PM