Ever since the introduction of Markowitz's classical quadratic programming problem, transforming portfolio optimization into a linear programming (LP) problem has drawn much attention from researchers and practitioners, given the tractability of LP. However, using non-linear risk measures and...

We evaluated the performance of multivariate models for forecasting Value at Risk (VaR), Expected Shortfall (ES) and Expectile Value at Risk (EVaR). We used Historical Simulation (HS), Dynamic Conditional Correlation-Generalized Autoregressive Conditional Heteroskedastic (DCC-GARCH) and copula...

We propose a family of range based risk measures to generalize the role of Value at Risk (VaR) in the formulation of Range Value at Risk (RVaR) considering other risk measures induced by a tail level. We discuss this type of measure in detail and its theoretical properties and representations....

Liquidity is easily perceived but not easily defined in financial markets. In this study, we present a class of liquidity measures called Proper Liquidity Measures (PLM). We prove that widely used measure such as percent quoted spreads and the Amihud measure fulfill our axioms. PLMs can be...