We extend the definition of a convex risk measure to a conditional framework where additional information is available. We characterize these risk measures through the associated acceptance sets and prove a representation result in terms of conditional expectations. As an example we consider the class of conditional entropic risk measures. A new regularity property of conditional risk measures ...

This chapter reviews the recent developments of Value at Risk (VaR) estimation. In this survey, the most available univariate and multivariate methods are presented. The robustness and accuracy of these estimation methods are investigated based on the simulated and real data. In the backtesting procedure, the conditional coverage test (Christoffersen 1998), the dynamic quantile test (Engle and ...

In management and planning it is a daily reality that more and more information is available gradually over time. It is well known that most risk measures (risk functionals) are time inconsistent in this situation in the following sense: it may happen that today some loss distribution appears to be less risky than another, but looking at the conditional distribution at a later time, the opposit...

Choosing a proper external risk measure is of great regulatory importance, as exemplified in the Basel II and Basel III Accords, which use value-at-risk with scenario analysis as the risk measures for setting capital requirements. We argue that a good external risk measure should be robust with respect to model misspecification and small changes in the data. A new class of data-based risk measu...

Stakeholder involvement and participation are widely recognized as being key success factors for IT risk assessment. A particular challenge facing current IT risk assessment methods is to provide accessible abstractions on matters of IT risk that attend to both managerial and technical perspectives of the stakeholders involved. In this paper, we investigate whether a conceptual modeling method ...

Free flight is an effective way to solve the congestions of air traffic flow. In order to guarantee the flight security, there is great significance to study on collision risk assessment in free flight. This paper applies the idea of collision risk of fixed route based on conflict area for reference, firstly designs a conflict area and establishes the collision risk model in free flight on the ...

A distortion risk measure used in finance and insurance is defined as the expected value of potential loss under a scenario probability measure. In this paper, the tail distortion risk measure is introduced to assess tail risks of excess losses modeled by the right tails of loss distributions. The asymptotic linear relation between tail distortion and Value-at-Risk is derived for heavy tailed l...

We consider the problem of optimizing a portfolio of n assets, whose returns are described by a joint discrete distribution. We formulate the mean–risk model, using as risk functionals the semideviation, deviation from quantile, and spectral risk measures. Using the modern theory of measures of risk, we derive an equivalent representation of the portfolio problem as a zero-sum matrix game, and ...

In this paper coherent risk measures and other currently used risk measures, notably Value-at-Risk (V aR), are studied from the perspective of the theory of coherent imprecise previsions. We introduce the notion of coherent risk measure defined on an arbitrary set of risks, showing that it can be considered a special case of coherent upper prevision. We also prove that our definition generalize...

This paper introduces a Value-at-Risk (VaR) model to generate route choices for a hazmat shipment based on a specified risk confidence level. The objective is to determine a route which minimizes the likelihood that the risk will be greater than a set threshold. Several properties of the VaR model are established. An exact solution procedure is proposed and tested to solve the single-trip probl...