Portfolio selection and risk management are very actively studied topics in quantitative finance and applied statistics. They are closely related to the dependency structure of portfolio assets or risk factors. The correlation structure across assets and opposite tail movements are essential to...

Systemic risk quantification in the current literature is concentrated on market-based methods such as CoVaR(Adrian and Brunnermeier (2016)). Although it is easily implemented, the interactions among the variables of interest and their joint distribution are less addressed. To quantify systemic...

We provide an extreme value analysis of the returns of Bitcoin. A particular focus is on the tail risk characteristics and we will provide an in-depth univariate extreme value analysis. Those properties will be compared to the traditional exchange rates of the G10 currencies versus the US...

In this paper we provide a review of copula theory with applications to finance. We illustrate the idea on the bivariate framework and discuss the simple, elliptical and Archimedean classes of copulae. Since the copulae model the dependency structure between random variables, next we explain the...

A compound Poisson distribution is a sum of independent and identically distributed random variables over a count variable that follows a Poisson distribution. Generally, its distribution is not tractable. However, it has many practical applications that require the estimation of the quantile...

We consider the expected shortfall of accounting values, or, mathematically speaking, of random variables that are not continuous (i. e. whose cumulative distribution function is not continuous). Acerbi and Tasche show that one has to abandon the conditional expectation in order to maintain...

One of the main challenges for the regulatory authorities in the aftermath of the last financial crisis is to define pragmatical and practicable risk concepts for the control and the regulation of systemic risks. They need for this purpose risk models that on one hand can capture the macro...