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...

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...

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...

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...

We propose a new approach to analyse the effect of diversification on a portfolio of risks. By means of mixing techniques, we provide an explicit formula for the probability density function of the portfolio. These techniques allow to compute analytically risk measures as VaR or TVaR, and...

Recent literature deals with bounds on the Value-at-Risk (VaR) of risky portfolios when only the marginal distributions of the components are known. In this paper we study Value-at-Risk bounds when the variance of the portfolio sum is also known, a situation that is of considerable interest in...

It is important to incorporate diverse heavy-tailed dependency between risks in estimating economic capital. Copulas can be a useful technique to capture dependence structure where extreme events occur simultaneously. Using the sample of U.S. property liability insurance industry, we examine the...

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...

This study arrives at a unifying risk measure for each of risk aversion and risk seeking preferences, a unifying risk measure (UrM) which explicitly embeds relative valuation of any two assets. The formal theory shows the UrM is, in relation to either of conditional volatility (CoV) or...