Value-at-risk (VaR) and conditional value-at-risk (CVaR) are important risk measures. They are often estimated by using importance sampling (IS) techniques. In this paper, we derive the asymptotic representations for IS estimators of VaR and CVaR. Based on these representations, we are able to prove the consistency and asymptotic normality of the estimators and to provide simple conditions unde...

We discuss linear regression approaches to the estimation of law-invariant conditional risk measures. Two estimation procedures are considered and compared; one is based on residual analysis of the standard least-squares method, and the other is in the spirit of the M-estimation approach used in robust statistics. In particular, value-at-risk and average valueat-risk measures are discussed in d...

F orecasting the volatility of a financial asset has wide implications in finance. Conditional variance extracted from the GARCH framework could be a suitable proxy of financial asset volatility. Option pricing, portfolio optimization, and risk management are examples of implications of conditional variance forecasting. One of the most recent methods of volatility forecasting is Real...

VALUE-AT-RISK IN RANKING CROP INSURANCE ALTERNATIVAES Abstract This study examines the use of conditional value-at-risk (CVaR) as a measure for evaluating risky alternatives. CVaR has been shown to have a number of advantages compared to the more traditionally applied value-at-risk in decision settings that involve choices among truncated revenue distributions. A conceptual presentation illustr...

Quantitative risk management (QRM, for short) is very important investors or financial institutions. This paper discusses portfolio selection in fuzzy environments by means of stochastic and methods. Two measures called hierarchical value-at-risk (HFVaR, conditional (HFCVaR, are proposed. And then models established based on the measure HFCVaR.