Η αξία κινδύνου και εφαρμογή της σε προβλήματα βελτιστοποίησης αναμενόμενων εσόδων χαρτοφυλακίου
Portfolio optimization problems under C-VaR constraints
In this paper an optimization or hedging approach for a portfolio of financial securities with view to reducing risk is considered. Effectiveness of this approach through examples and applications is also presented. In particular we focus on the optimization of what is known as "Conditional Value-at-Risk (C-VaR)", and a comparison with the corresponding Value-at-Risk (VaR) optimization will be exploited. C-VaR is defined as the expected loss that exceeds the VaR, and portfolios with low C-VaR have a necessarily and low VaR. The central idea of our approach is to optimize a portfolio that calculates VaR and at the same time optimizes C-VaR with or without limitations. In addition, this approach is applied to maximize expected returns under consideration of specific C-VaR constraints. This method is widely used by investment companies, brokerage firms, as well as by mutual funds or companies in which the risk is involved. Finally, an example as an application of our approach to a portfolio of S&P 100 shares and useful feedback and conclusions will be given.