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....

Using sectorial indices of the Brazilian market, we compare the portfolio optimization approach known as risk parity with minimum variance and equally weighted approaches. We apply various estimators for the covariance matrix to each portfolio strategy, since portfolio variance is considered as...