An intensive and still growing body of research focuses on estimating a portfolio’s Value-at-Risk.Depending on both the degree of non-linearity of the instruments comprised in the portfolio and thewillingness to make restrictive assumptions on the underlying statistical distributions, a...

We present dynamic trading strategies that target a predefined level of risk measured by volatility, Value-at-Risk (VaR) or Conditional-Value-at-Risk (CVaR). Recent studies have shown that volatility targeting increases the risk-adjusted performance and heightens utility gains for mean-variance...

This paper examines optimal portfolio selection using quantile-based risk measures such as Valueat-Risk (VaR) and Conditional Value-at-Risk (CVaR). We address the case of a singular covariance matrix of asset returns, which leads to an optimization problem with infinitely many solutions. An...

Recent Value-at-Risk (VaR) models based on historical simulation often incorporate approaches where the volatility of the historical sample is rescaled or filtered to better reflect current market conditions. These filtered historical simulation (FHS) VaR models are now widely used in the...

This paper discusses the value-at-risk (VaR) concept and assesses the financial adequacy of the price probability determined by frequency of trades at price p. We take the price definition as the ratio of executed trade value to volume and show that it leads to price statistical moments, which...

We consider the VaR associated with the global loss generated by a set risk sources. We propose a sequence of simple models incorporating progressively the notions of contagion due to instantaneous correlations, of serial correlation, of evolution of the instantaneous correlations, of volatility...

We study endogenous leverage in a general equilibrium model with incomplete markets. We prove that in any binary tree leverage emerges in equilibrium at the maximum level such that VaR=0, so there is no default in equilibrium, provided that agents get no utility from holding the collateral. When...