An acceptability measure is a number that summarizes information on monetary outcomes of a given position in various scenarios, and that, depending on context, may be interpreted as a capital requirement or as a price. In a multiperiod setting, it is reasonable to require that an acceptability measure should satisfy certain conditions of time consistency. Various notions of time consistency may...

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...

Consider a portfolio of n obligors such as loans, corporate bonds and other instruments subject to possible default. Tang and Yuan (2012, Submitted) introduced a new model for the loss given default and studied its tail behavior, Value at Risk, and Conditional Tail Expectation under the assumption that the losses jointly follow a multivariate regularly varying distribution. However, in the case...

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 ...

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.

Value at Risk (VaR) has emerged in recent years as a standard tool to measure and control the risk of trading portfolios. Yet, existing theoretical analyses of the optimal behavior of a trader subject to VaR limits have produced a negative view of VaR as a risk-control tool. In particular, VaR limits have been found to induce increased risk exposure in some states and an increased probability o...

Based on credibilistic value-at-risk (CVaR) of regularfuzzy variable, we introduce a new CVaR reduction method fortype-2 fuzzy variables. The reduced fuzzy variables arecharacterized by parametric possibility distributions. We establishsome useful analytical expressions for mean values and secondorder moments of common reduced fuzzy variables. The convex properties of second order moments with ...

Tail conditional expectations refer to the expected values of random variables conditioning on some tail events and are closely related to various coherent risk measures. In the univariate case, the tail conditional expectation is asymptotically proportional to the value-at-risk, a popular risk measure. The focus of this paper is on asymptotic relations between the multivariate tail conditional...