Two main axiomatically based risk measures are the coherent risk measure, which assumes subadditivity for random variables, and the insurance risk measure, which assumes additivity for comonotonic random variables. We propose a new, data based, risk measure, called natural risk statistic, that is characterized by a new set of axioms. The new axioms only require subadditivity for comonotonic ran...

We estimate Value-at-Risk for sums of dependent random variables. We model multivariate dependent random variables using archimedean copulas. This structure allows one to calculate the asymptotic behaviour of extremal events. An important application of such results are Value-at-Risk estimates for sums of dependent random variables.

its most compelling aspect is its vertical variation, that is, the sum of the vertical distances between its adjacent terms. Denoted by varw, the vertical variation of the sequence in (1.1) is varw = 2 + 1 + 0 + 2 + 1 = 6. Our purpose here is to compute the mean and variance of var on four classical sets of combinatorial sequences. To formalize matters and place our problem in the context of ot...

I show that the structure of the firm is not neutral in respect to regulatory capital budgeted under rules which are based on the Value-at-Risk.

The aim of this paper is to discuss the use of the Generalized Hyperbolic Distributions to fit Brazilian assets returns. Selected subclasses are compared regarding goodness of fit statistics and distances. Empirical results show that these distributions fit data well. Then we show how to use these distributions in value at risk estimation and derivative price computation.

Introduction Conclusions References

This article is devoted to the study cashflow maps used in the computation of value-at-risk (VaR). Properties and characteristics of the approaches found in the literature are presented and two new approaches are introduced. The goal of this paper is to study the quality of these maps. This is done by calculating the risk induced by the difference between the mapped cashflows and the original one.