A recent paper by Prékopa (2012) presented results in connection with Multivariate Value-at-Risk (MVaR) that has been known for some time under the name of p-quantile or p-Level Efficient Point (pLEP) and introduced a new multivariate risk measure, called Multivariate Conditional Value-at-Risk (MCVaR). The purpose of this paper is to further develop the theory and methodology of MVaR and MCVaR....

In this paper, the large deviation approach for computing the capital charge for operational risk of a bank is explored. Firstly, the negatively-associated structure is utilized to measure the dependence between distinct operational loss cells. Secondly, the lower and upper bounds of the tail distribution function of total aggregated loss processes are determined. In addition, first order appro...

Denote by X the set of actuarial risks, and let 0 ≤ X ∈ X be a random variable rv with cumulative distribution function cdf F x , decumulative distribution function ddf F x 1 − F x , and probability density function pdf f x . The functional H : X → 0,∞ is then referred to as a risk measure, and it is interpreted as the measure of risk inherent in X. Naturally, a quite significant number of risk...

Risk adjusted performance measurement for a portfolio involves calculating the contributions to total economic capital for sub-portfolios or single assets. We show that there is only one definition for the contributions which is suitable for performance measurement, namely as derivative of the underlying risk measure with respect to the weight of the considered sub-portfolio or asset. We review...

In credit risk management, migration or transition matrices are major inputs for risk management, Credit Value-at-Risk or derivative pricing. After reviewing distance measures for migration matrices we propose some new directed difference indices to measure changes in migration behavior in a more risk-sensitive way. We quantify the changes of the classical distance measures and the new distance...

Maximum Relative Drawdown measures the largest percentage drop of the price process on a given time interval. Recently, Maximum Relative Drawdown has become more popular as an alternative measure of risk. In contrast to the Value at Risk measure, it captures the path property of the price process. In this article, we propose a partial differential equation approach to determine the theoretical ...

Incorporating the Poisson jumps and exchange rate risk, this paper provides an analytical VaR to manage market risk of international portfolios over the subprime mortgage crisis. There are some properties in the model. First, different from past studies in portfolios valued only in one currency, this model considers portfolios not only with jumps but also with exchange rate risk, that is vital ...

Risks faced by traders from price movements are sometimes magni¿ed by the actions of other traders. Risk management systems which neglect this feature may give a seriously misleading picture of the true risks. The hazards arising from this potential blindspot are at their most dangerous when the prevailing conventional wisdom lulls traders into a false sense of security on the attractivenss of ...

We propose an extension of the CPPI method, which is based on conditional floors. In this framework, we examine in particular the margin based strategies. This method allows to keep part of the past gains and to protect the portfolio value against future high drawdowns of the financial market. However, as for the standard CPPI method, the investor can benefit from potential market rises. To con...

Related to the current discussion of value-at-risk-based capital allocation and performance management (RAPM) for managing bank capital, a risk theoretical RAPM-approach for propertylliability-insurance companies is presented. The paper discusses several central issues of a RAPM-approach: Virtual risk adjusted capital (VRAC) on the company level, return on risk adjusted capital (RORAC), risk ba...