During early phases of open-pit mining production planning many parameters are uncertain, and since the mining operation is performed only once, any evaluations based only on on average outcomes neglects the very real chance of obtaining an outcome that is below average. Taking into account also that operation costs are considerable and the mining horizon usually extends over several decades it...

Probabilistic and quantile (percentile) functions are commonly used for the analysis of models with uncertainties or variabilities in parameters. In nancial applications, the percentile of the losses is called Value-at-Risk (VaR). VaR, a widely used performance measure, answers the question: what is the maximum loss with a speci ed con dence level? Percentiles are also used for de ning other re...

Assuming absolute continuity of marginals, we give the distribution for sums of dependent random variables from some class of Archimedean copulas and the marginal distribution functions of all order statistics.We use conditional independence structure of random variables from this class of Archimedean copulas and Laplace transform. Additionally, we present an application of our results to VaR e...

Fundamental properties of conditional value-at-risk (CVaR), as a measure of risk with significant advantages over value-at-risk (VaR), are derived for loss distributions in finance that can involve discreetness. Such distributions are of particular importance in applications because of the prevalence of models based on scenarios and finite sampling. CVaR is able to quantify dangers beyond VaR a...

An asymmetric multivariate generalization of the recently proposed class of normal mixture GARCH models is developed. Issues of parametrization and estimation are discussed. Conditions for covariance stationarity and the existence of the fourth moment are derived, and expressions for the dynamic correlation structure of the process are provided. In an application to stock market returns, it is ...

A formula for the conditional value-at-risk of classical portfolio insurance is derived and shown to be constant for sufficiently small loss probabilities. As illustrations, we discuss portfolio insurance for an equity market index using empirical data, and analyze the more general multivariate situation of a portfolio of risky assets. 1. Introduction. Portfolio insurance, introduced by Leland ...

An adaptive direct numerical integration (DNI) algorithm is developed for inverting characteristic functions of compound distributions, enabling efficient computations of high quantiles and conditional Value at Risk (CVaR). A key innovation of the numerical scheme is an effective tail integration approximation that reduces the truncation errors significantly. High precision results of the 0.999...

In portfolio management, Robust Conditional Value at Risk (Robust CVaR) has been proposed to deal with structured uncertainty in the estimation of the assets probability distribution. Meanwhile, regularization in portfolio optimization has been investigated as a way to construct portfolios that show satisfactory out-ofsample performance under estimation error. In this paper, we prove that optim...

Abstract Conditional value-at-risk (CVaR) and conditional expected shortfall (CES) are widely adopted risk measures which help monitor potential tail while adapting to evolving market information. In this paper, we propose an approach constructing simultaneous confidence bands (SCBs) for as measured by CVaR CES, with the uniformly valid a set of levels. We consider one-sided (downside or upside...

A new one-parameter family of risk measures called Conditional Drawdown (CDD) has been proposed. These measures of risk are functionals of the portfolio drawdown (underwater) curve considered in active portfolio management. For some value of the tolerance parameter α, in the case of a single sample path, drawdown functional is defined as the mean of the worst (1 − α) ∗ 100% drawdowns. The CDD m...