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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…
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…
We address the problem that classical risk measures may not detect the tail risk adequately. This can occur for instance due to averaging when calculating the Expected Shortfall. The current literature proposes the so-called adjusted…
Effect size measures and visualization techniques aimed at maximizing the interpretability and comparability of results from statistical models have long been of great importance and are recently again receiving increased attention in the…
This paper concerns sequential computation of risk measures for financial data and asks how, given a risk measurement procedure, we can tell whether the answers it produces are `correct'. We draw the distinction between `external' and…
Despite decades of research in risk management, most of the literature has focused on scalar risk measures (like e.g. Value-at-Risk and Expected Shortfall). While such scalar measures provide compact and tractable summaries, they provide a…
This research presents a framework for quantitative risk management in volatile markets, specifically focusing on expectile-based methodologies applied to the FTSE 100 index. Traditional risk measures such as Value-at-Risk (VaR) have…
The financial crisis has dramatically demonstrated that the traditional approach to apply univariate monetary risk measures to single institutions does not capture sufficiently the perilous systemic risk that is generated by the…
The paper concerns primal and dual representations as well as time consistency of set-valued dynamic risk measures. Set-valued risk measures appear naturally when markets with transaction costs are considered and capital requirements can be…
The inf-convolution of risk measures is directly related to risk sharing and general equilibrium, and it has attracted considerable attention in mathematical finance and insurance problems. However, the theory is restricted to finite sets…
We axiomatically introduce risk-consistent conditional systemic risk measures defined on multidimensional risks. This class consists of those conditional systemic risk measures which can be decomposed into a state-wise conditional…
A different general philosophy, to be called Full Randomness (FR), for the analysis of random effects models is presented, involving a notion of reducing or preferably eliminating fixed effects, at least formally. For example, under FR…
We analyze the performance of RiskMetrics, a widely used methodology for measuring market risk. Based on the assumption of normally distributed returns, the RiskMetrics model completely ignores the presence of fat tails in the distribution…
Optimizing risk measures such as Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR) of a general loss distribution is usually difficult, because 1) the loss function might lack structural properties such as convexity or…
The importance of quality measures in process mining has increased. One of the key quality aspects, generalization, is concerned with measuring the degree of overfitting of a process model w.r.t. an event log, since the recorded behavior is…
Conditional Value-at-Risk (CoVaR) quantifies systemic financial risk by measuring the loss quantile of one asset, conditional on another asset experiencing distress. We develop a Transformer-based methodology that integrates financial news…
Backtesting risk measures is a central task in financial regulation. While standard backtests evaluate whether a forecasting model is statistically consistent with observed losses, regulatory practice often requires assessing the…
We introduce a general framework for measuring risk in the context of Markov control processes with risk maps on general Borel spaces that generalize known concepts of risk measures in mathematical finance, operations research and…
We study issues of robustness in the context of Quantitative Risk Management and Optimization. We develop a general methodology for determining whether a given risk measurement related optimization problem is robust, which we call…
Systemic risk refers to the risk that the financial system is susceptible to failures due to the characteristics of the system itself. The tremendous cost of systemic risk requires the design and implementation of tools for the efficient…