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The risk of a financial position is usually summarized by a risk measure. As this risk measure has to be estimated from historical data, it is important to be able to verify and compare competing estimation procedures. In statistical…
Analytical, free of time consuming Monte Carlo simulations, framework for credit portfolio systematic risk metrics calculations is presented. Techniques are described that allow calculation of portfolio-level systematic risk measures…
We develop a generalized stability framework for stochastic discrete-time systems, where the generality pertains to the ways in which the distribution of the state energy can be characterized. We use tools from finance and operations…
Uncertainty is prevalent in engineering design, data-driven problems, and decision making broadly. Due to inherent risk-averseness and ambiguity about assumptions, it is common to address uncertainty by formulating and solving conservative…
In this paper, we consider a situation where a decision maker's (DM's) risk preference can be described by a spectral risk measure (SRM) but there is not a single SRM which can be used to represent the DM's preferences consistently.…
Several new geometric quantile-based measures for multivariate dispersion, skewness, kurtosis, and spherical asymmetry are defined. These measures differ from existing measures, which use volumes and are easy to calculate. Some theoretical…
By means of the techniques of Boolean valued analysis, we provide a transfer principle between duality theory of classical convex risk measures and duality theory of conditional risk measures. Namely, a conditional risk measure can be…
Different approaches to defining dynamic market risk measures are available in the literature. Most are focused or derived from probability theory, economic behavior or dynamic programming. Here, we propose an approach to define and…
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…
Spectral risk measures are attractive risk measures as they allow the user to obtain risk measures that reflect their risk-aversion functions. To date there has been very little guidance on the choice of risk-aversion functions underlying…
Law-invariant functionals are central to risk management and assign identical values to random prospects sharing the same distribution under an atomless reference probability measure. This measure is typically assumed fixed. Here, we adopt…
The study of systemic risk is often presented through the analysis of several measures referring to quantities used by practitioners and policy makers. Almost invariably, those measures evaluate the size of the impact that exogenous events…
In this paper we present results on dynamic multivariate scalar risk measures, which arise in markets with transaction costs and systemic risk. Dual representations of such risk measures are presented. These are then used to obtain the main…
In this paper, we study general monetary risk measures (without any convexity or weak convexity). A monetary (respectively, positively homogeneous) risk measure can be characterized as the lower envelope of a family of convex (respectively,…
Multifractal systems usually have singularity spectra defined on bounded sets of H\"older exponents. As a consequence, their associated multifractal scaling exponents are expected to depend linearly upon statistical moment orders at high…
Measuring the contribution of a bank or an insurance company to overall systemic risk is a key concern, particularly in the aftermath of the 2007--2009 financial crisis and the 2020 downturn. In this paper, we derive worst-case and…
Since risky positions in multivariate portfolios can be offset by various choices of capital requirements that depend on the exchange rules and related transaction costs, it is natural to assume that the risk measures of random vectors are…
Risk and utility functionals are fundamental building blocks in economics and finance. In this paper we investigate under which conditions a risk or utility functional is sensitive to the accumulation of losses in the sense that any…
Spectral risk measures are attractive risk measures as they allow the user to obtain risk measures that reflect their subjective risk-aversion. This paper examines spectral risk measures based on an exponential utility function, and finds…
We report on an experimental observation of classical diffusion distinguishing between structural universality classes of disordered systems in one dimension. Samples of hyperuniform and short-range disorder were designed, characterized by…