The theory of copulae is known to provide a useful tool for modelling dependence in integrated risk management. In the present paper we review and extend some of the more recent results for finding distributional bounds for functions of dependent risks. As an example, the main emphasis is put on Value-at-Risk as a risk measure.

In the last few decades, risk managers have truly experienced a revolution. The rapid increase in the usage of risk management techniques has spread well beyond derivatives and is totally changing the way institutions approach their financial risk. In response to the financial disasters of the early 1990s a new method called VaR (Value at Risk) was developed as a simple method to quantify marke...

South Africa assumes a significant position in the insurance landscape of Africa. The present research based upon qualitative and quantitative analysis, shows that it shows the characteristics of a Complex Adaptive System. In addition, a statistical analysis of risk measures through Value at risk and Conditional tail expectation is carried out to show how an individual insurance company copes u...

In this study, we analyze the aerospace stocks prices in order to characterize the sector behavior. The data analyzed cover the period from January 1987 to April 1999. We present a new index for the aerospace sector and we investigate the statistical characteristics of this index. Our results show that this index is well described by Tsallis distribution. We explore this result and modify the s...

This paper investigates optimal portfolio and wealth strategy of an institutional investor under the Value-at-Risk (VaR) constraint in an economy under jump diffusion. We show that overlooking or underestimating jump risk factor could be the cause of failure to satisfy the VaR constraint in the recent financial crisis for many financial institutions. We also find that the introduction of the ju...

In this paper, we introduce two alternative extensions of the classical univariate Value-at-Risk (VaR) in a multivariate setting. The two proposed multivariate VaR are vector-valued measures with the same dimension as the underlying risk portfolio. The lower-orthant VaR is constructed from level sets of multivariate distribution functions whereas the upper-orthant VaR is constructed from level ...

An investigation of the limiting behavior of a risk capital allocation rule based on the Conditional Tail Expectation (CTE) risk measure is carried out. More specifically, with the help of general notions of Extreme Value Theory (EVT), the aforementioned risk capital allocation is shown to be asymptotically proportional to the corresponding Value-at-Risk (VaR) risk measure. The existing methodo...

Abstract. We investigate properties of a version of tail comonotonicity that can be applied to absolutely continuous distributions, and give several methods for constructions of multivariate distributions with tail comonotonicity or strongest tail dependence. Archimedean copulas as mixtures of powers, and scale mixtures of a non-negative random vector with the mixing distribution having slowly ...

In order to protect stakeholders of insurance companies and financial institutions against adverse outcomes of risky businesses, regulators and senior management use capital allocation techniques. For enterprise-wide risk management, it has become important to calculate the contribution of each risk within a portfolio. For that purpose, bivariate lower and upper orthant tail value-at-risk can b...