Graduate Student Seminar

Speaker 1: Hyekyung Park

Title

Robust portfolio selection problem with Value-at-risk (VaR) constraint

Abstract

Consider a portfolio selection problem that invests $1 into a given n number of assets. We want to maximize our return on the portfolio while the probability of losing a given percentage on the portfolio is less than a given bound. The probability constraint is called the Value-at-risk (VaR) constraint or chance constraint. In practice, future returns and the distribution of the returns are unknown and random. Hence, we define a random variable vector of returns by using a linear factor model and then assume that the return vector is a multivariate normal distribution. We compare the problem under separable uncertainty sets of variables with the problem under a joint ellipsoidal uncertainty set by providing the computational results with real market data of 42 assets and 10 factors for multi-period. Currently, we’re working on an extension to the multi-period case under the joint uncertainty set.

Speaker 2: Juyoung Jeong

Title

The Transfer Principle and Metaformulas of the Inverse Eigenvalue Mapping on the Set of Permutation Invariant Sets

Abstract

The eigenvalue mapping, which takes a symmetric matrix to the vector of its eigenvalues in decreasing order, is not linear nor convex in general. This makes it difficult to study various properties related to eigenvalues. However, in this seminar, we show that the inverse of the eigenvalue mapping on the set of permutation invariant sets has linear structure. We also discuss some transfer principles and related metaformulas between permutation invariant functions and spectral functions.