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...

Financial institutions define their marginal cost of risk on the basis of the gradients of arbitrarily chosen risk measures. We reverse this approach by calculating the marginal cost for a profit-maximizing firm with risk-averse counterparties, and then identifying the risk measure delivering the correct marginal cost. The resulting measure is a weighted average of three parts, each correspondi...

The banking systems that deal with risk management depend on underlying risk measures. Following the recommendation of the Basel II accord, most banks have developed internal models to determine their capital requirement. The Value at Risk measure plays an important role in computing this capital. In this paper we analyze in detail the errors produced by the use of this measure. We then discuss...

We discuss recent advances in the mathematical quantification of financial risk. The standard approach in terms of Value at Risk has serious deficiencies. This has motivated a systematic analysis of risk measures which satisfy some minimal requirements of coherence and consistency. Our focus will be on the basic structure theorems for convex risk measures, on the role of law-invariance, and on ...

One of the major problem faced by banks is how to manage the risk exposure in large portfolios. According to Basel II regulation banks has to measure the risk using Value-at-Risk with confidence level 99%. However, this regulation does not specify the way to calculate Valueat-Risk. The easiest way to calculate Value-at-Risk is to assume that portfolio returns are normally distributed. Altough, ...

The purpose of this paper is to review the recent derivatives security research involving liquidity risk and to summarize its implications for practical risk management. The literature supports three general conclusions. The first is that the classical option price is "on average" true, even given liquidity risk. Second, it is well known that although the classical (theoretical) option hedge ca...

This article highlights the importance of investors’downside-risk concerns, and examines optimal investment behaviors in a dynamic downside-risk framework. The authors does not only derive an analytical expression of investors’ optimal behaviors, but also provide economic insights of the properties of the downside risk measure and optimal investment strategies using comparative statics. It shed...

A risk-metric framework that supports Enterprise Risk Management is described. At the heart of the framework is the notion of a risk profile that provides risk measurement for risk elements. By providing a generic template in which metrics can be codified in terms of metric space operators, risk profiles can be used to construct a variety of risk measures for different business contexts. These ...

Article history: Received 29 August 2012 Received in revised form 21 May 2013 Accepted 6 August 2013 Available online 15 August 2013 We test the impact of idiosyncratic risk on stock returns for emerging markets that experience financial market liberalizations. Idiosyncratic risk is positively associated with returns prior to financial market liberalization, but liberalization diminishes this e...