The classical Lévy-Cramér continuity theorem asserts that the convergence of the characteristic functions implies the weak convergence of the corresponding probability measures. We extend this result to the setting of non-commutative probability theory and discuss some applications. ∗CNRS, Université de Provence, Université de la Méditerranée, Université du Sud Toulon-Var. 2 V. Jakšić, Y. Pautr...

C. neoformans is a basidiomycetous, yeast-like fungus that, following inhalation from an environmental source, causes respiratory and neurological infection in humans and animals. This fungus has 5 serotypes (A, B, C, D, and AD), and recently was subdivided into 3 varieties known as C. neoformans var. grubii (serotype A), C. neoformans var. neoformans (serotype D), and C. neoformans var. gattii...

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Özet. Maliyet ve bütçe tahminleri, süreç kıyaslama ve proje kontrolü gibi yazılım proje yönetimi aktivitelerinin pek çoğu yazılım işlevsel büyüklük ölçümlerine bağlı olduğu için bu değerin ölçümü ve güvenilirliği çok önemlidir. Bu sebeple, İşlevsel büyüklük ölçümlerin güvenilirliğini artırmak için, ölçüm sürecinin sonunda büyüklük dokümanları kontrol edilmeli ve gözden geçirilmelidir. Ancak, öl...

Assuming absolute continuity of marginals, we give the distribution for sums of dependent random variables from some class of Archimedean copulas and the marginal distribution functions of all order statistics.We use conditional independence structure of random variables from this class of Archimedean copulas and Laplace transform. Additionally, we present an application of our results to VaR e...

The worst-possible Value-at-Risk for a non-decreasing function of dependent risks is known when or the copula of the portfolio is bounded from below. In this paper we analyze the properties of the dependence structures leading to this solution, in particular their form and the implied functional dependence between the marginals. Furthermore, we criticise the assumption of the worst-possible sce...

We discuss the coherence properties of Expected Shortfall (ES) as a financial risk measure. This statistic arises in a natural way from the estimation of the “average of the 100p% worst losses” in a sample of returns to a portfolio. Here p is some fixed confidence level. We also compare several alternative representations of ES which turn out to be more appropriate for certain purposes.

Gold has been recognized as the most important precious metals in the human society. Other than as a medium of exchange, gold has been a consumption and investment product for a long history. It has been recognized a well-positive role in portfolio performance by many financial market practitioners. During the recent financial crisis, gold spot prices have exhibited significant volatility. Thus...

ARCH and GARCH models are widely used to model financial market volatilities in risk management applications. Considering a GARCH model with heavy-tailed innovations, we characterize the limiting distribution of an estimator of the conditional Value-at-Risk (VaR), which corresponds to the extremal quantile of the conditional distribution of the GARCH process. We propose two methods, the normal ...

In this paper we test several risk management models for computing expected shortfall for one-period hedge errors of hedged derivatives positions. Contrary to value-at-risk, expected shortfall cannot be tested using the standard binomial test, since we need information of the distribution in the tail. As derivatives positions change characteristics and thereby the size of risk exposures over ti...