Risk Modeling in Optimization Problems via Value at Risk, Conditional Value at Risk, and Its Robustification

Abstract

In this chapter, we explore the portfolio selection problem involving uncertainty, in other words: risk. To deal with this uncertainty, we will utilize Value at Risk (VaR) and Conditional Value at Risk (CVaR). Moreover, we present a Robust Optimization method for specifying the parameter uncertainty while minimizing the Conditional Value at Risk. We investigate optimization problems in order to minimize CVaR. Our approach consists in the use of robust optimization techniques for minimization of CVaR. We research Robust CVaR (RCVaR) optimization models under ellipsoidal uncertainty. Finally, we conclude that one can control the parameteric uncertainty with some robust distribution assumptions and obtain certain optimal solutions.