Related papers: Spatial risk measures and applications to max-stab…
Max-stable random fields play a central role in modeling extreme value phenomena. We obtain an explicit formula for the conditional probability in general max-linear models, which include a large class of max-stable random fields. As a…
This paper addresses the problem of recovering the spatial market potential of a retail product from spatially distributed sales data. In order to tackle the problem in a general way, the concept of spatial potential is introduced. The…
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…
The relationship between set-valued risk measures for processes and vectors on the optional filtration is investigated. The equivalence of risk measures for processes and vectors and the equivalence of their penalty function formulations…
An exceedance region is the set of locations in a spatial domain where a process exceeds some threshold. Examples of exceedance regions include areas where ozone concentrations exceed safety standards, there is high risk for tornadoes or…
Power grid expansion planning requires making large investment decisions in the present that will impact the future cost and reliability of a system exposed to wide-ranging uncertainties. Extreme temperatures can pose significant challenges…
Max-stable processes provide natural models for the modelling of spatial extreme values observed at a set of spatial sites. Full likelihood inference for max-stable data is, however, complicated by the form of the likelihood function as it…
We investigate to which extent the relevant features of (static) Systemic Risk Measures can be extended to a conditional setting. After providing a general dual representation result, we analyze in greater detail Conditional Shortfall…
A new measure to characterize stability of complex dynamical systems against large perturbation is suggested, the stability threshold (ST). It quantifies the magnitude of the weakest perturbation capable to disrupt the system and switch it…
Risk measures for multivariate financial positions are studied in a utility-based framework. Under a certain incomplete preference relation, shortfall and divergence risk measures are defined as the optimal values of specific set…
We establish a theory for multivariate extreme value analysis of dynamical systems. Namely, we provide conditions adapted to the dynamical setting which enable the study of dependence between extreme values of the components of…
We develop a risk-averse safety analysis method for stochastic systems on discrete infinite time horizons. Our method quantifies the notion of risk for a control system in terms of the severity of a harmful random outcome in a fraction of…
We introduce a novel class of systemic risk measures, the Vulnerability Conditional risk measures, which try to capture the "tail risk" of a risky position in scenarios where one or more market participants is experiencing financial…
Max-stable processes have proved to be useful for the statistical modelling of spatial extremes. Several representations of max-stable random fields have been proposed in the literature. One such representation is based on a limit of…
The purpose of the research presented in this article is to develop a dynamic system for forecasting and minimizing the risks of an industrial company based on their quantitative assessment. The article considers the conceptual apparatus of…
Climate-related phenomena are increasingly affecting regions worldwide, manifesting as floods, water scarcity, and heat waves, significantly impairing companies' assets and productivity. It is essential for asset managers to quantify the…
The definition of complexity through Statistical Complexity Measures (SCM) has recently seen major improvements. Mostly, effort is concentrated in measures on time series. We propose a SCM definition for spatial dynamical systems. Our…
As a rule statistical measures are often vulnerable to the presence of outliers and spatial correlation coefficients, critical in the assessment of spatial data, remain susceptible to this inherent flaw. In contexts where data originates…
Extreme events with potential deadly outcomes, such as those organized by terror groups, are highly unpredictable in nature and an imminent threat to society. In particular, quantifying the likelihood of a terror attack occurring in an…
Risk measures such as Expected Shortfall (ES) and Value-at-Risk (VaR) have been prominent in banking regulation and financial risk management. Motivated by practical considerations in the assessment and management of risks, including…