Graduate Student Seminar

Speaker 1: Teresa Lebair

Title

Shape Constrained B-Spline Estimation

Abstract

Shape constrained estimators receive considerable attention, motivated by many important applications in science and engineering.  In this presentation, we consider a B-spline estimator subject to general derivative constraints.  The goal of our research is to show that this estimator is an optimal minimax estimator with respect to the supremum norm.  This can be done by (i) establishing a critical uniform Lipschitz property of the B-spline estimator and (ii) demonstrating that each sufficiently smooth function subject to a certain derivative constraint can be approximated accurately enough by a B-spline that adheres to the same derivative constraint.  We will discuss the progress and challenges related to this research in this presentation.

Speaker 2: Hye-kyung Park

Title

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

Abstract

Consider a portfolio selection problem that invests $1 in to a given n number of assets. We want to maximize our return on the portfolio while the probability of that losing a given percentage $\delta$ on the portfolio is less than a given bound $\epsilon$. The probability constraint is called Value-at-risk (VaR) constraint or chance constraint. In practice, future returns and the distribution of the returns are unknown and random. So we define a random variable return vector of returns vector by using a linear factor model and then assumed 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 datas of 42 assets and 10 factors for multi-period.