Selecting the optimal Markowitz portfolio depends on estimating the covariance matrix of the
returns of N assets from T periods of historical data. Problematically, N is typically of the …

This article develops a nonparametric varying-coefficient approach for modeling the
expectile-based value at risk (EVaR). EVaR has an advantage over the conventional …

This article develops a single-index approach for modeling the expectile-based value at risk
(EVaR). EVaR has an advantage over the conventional quantile-based VaR (QVaR) of …

In this study, we derive analytic expressions for the elliptical truncated moment generating
function (MGF), the zeroth-, first-, and second-order moments of quadratic forms of the …

The saddlepoint method of approximation is attributed to Daniels (1954), and can be
described in basic terms as yielding an accurate and usually fast and very numerically …

Computable expressions are derived for the Expected Shortfall of portfolios whose value is a
quadratic function of a number of risk factors, as arise from a Delta–Gamma–Theta …

We provide an accurate closed-form expression for the expected shortfall of linear portfolios
with elliptically distributed risk factors. Our results aim to correct inaccuracies that originate in …

Risk management today focuses heavily on estimating the location and conditional
expectation of the left tail of the probability distribution for returns or portfolio value. The Holy …

Purpose The purpose of this paper is to present the method for efficient computation of risk
measures using Fourier transform technique. Another objective is to demonstrate that this …

We consider multi-step algorithms for the computation of the historical expected shortfall. At
each step of the algorithms, we use Monte Carlo simulations to reduce the number of …