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We describe a general framework for measuring risks, where the risk measure takes values in an abstract cone. It is shown that this approach naturally includes the classical risk measures and set-valued risk measures and yields a natural…

Probability · Mathematics 2008-12-02 Ignacio Cascos , Ilya Molchanov

This paper revisits and extends the 2013 development by Rockafellar and Uryasev of the Risk Quadrangle (RQ) as a unified scheme for integrating risk management, optimization, and statistical estimation. The RQ features four…

Optimization and Control · Mathematics 2026-03-31 Bogdan Grechuk , Anton Malandii , Terry Rockafellar , Stan Uryasev

The fragility of financial systems was starkly demonstrated in early 2023 through a cascade of major bank failures in the United States, including the second, third, and fourth largest collapses in the US history. The highly interdependent…

Risk Management · Quantitative Finance 2024-11-19 Kamil Fortuna , Janusz Szwabiński

Modern society heavily relies on strongly connected, socio-technical systems. As a result, distinct risks threatening the operation of individual systems can no longer be treated in isolation. Consequently, risk experts are actively seeking…

Risk Management · Quantitative Finance 2018-02-07 Christos Ellinas , Neil Allan , Caroline Coombe

Several authors have recently developed risk-sensitive policy gradient methods that augment the standard expected cost minimization problem with a measure of variability in cost. These studies have focused on specific risk-measures, such as…

Artificial Intelligence · Computer Science 2015-06-09 Aviv Tamar , Yinlam Chow , Mohammad Ghavamzadeh , Shie Mannor

In this paper, we present a unified framework for decision making under uncertainty. Our framework is based on the composite of two risk measures, where the inner risk measure accounts for the risk of decision given the exact distribution…

Optimization and Control · Mathematics 2015-01-07 Pengyu Qian , Zizhuo Wang , Zaiwen Wen

Stacking regressions is an ensemble technique that forms linear combinations of different regression estimators to enhance predictive accuracy. The conventional approach uses cross-validation data to generate predictions from the…

Machine Learning · Statistics 2024-10-10 Xin Chen , Jason M. Klusowski , Yan Shuo Tan

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…

Risk Management · Quantitative Finance 2025-11-28 Michele Bonollo , Martino Grasselli , Gianmarco Mori , Havva Nilsu Oz

Quantifying the similarity between two mathematical structures or datasets constitutes a particularly interesting and useful operation in several theoretical and applied problems. Aimed at this specific objective, the Jaccard index has been…

Machine Learning · Computer Science 2021-11-19 Luciano da F. Costa

As interconnected systems proliferate, safeguarding complex infrastructures against an escalating array of cyber threats has become an urgent challenge. The increasing number of vulnerabilities, combined with resource constraints, makes…

Cryptography and Security · Computer Science 2025-02-18 Yuning Jiang , Nay Oo , Qiaoran Meng , Hoon Wei Lim , Biplab Sikdar

Aggregate shocks affect most households' and firms' decisions. Using three stylized models we show that inference based on cross-sectional data alone generally fails to correctly account for decision making of rational agents facing…

Methodology · Statistics 2022-04-28 Jinyong Hahn , Guido Kuersteiner , Maurizio Mazzocco

Assessing systemic risk in financial markets is of great importance but it often requires data that are unavailable or available at a very low frequency. For this reason, systemic risk assessment with partial information is potentially very…

Risk Management · Quantitative Finance 2018-08-01 Domenico Di Gangi , Fabrizio Lillo , Davide Pirino

Cyber risk assessment is a fundamental activity for enhancing the protection of an organization, identifying and evaluating the exposure to cyber threats. Currently, this activity is carried out mainly manually and the identification and…

Cryptography and Security · Computer Science 2022-07-08 Marco Angelini , Silvia Bonomi , Alessandro Palma

An important role carried out by cyber-security experts is the assessment of proposed computer systems, during their design stage. This task is fraught with difficulties and uncertainty, making the knowledge provided by human experts…

Artificial Intelligence · Computer Science 2016-08-31 Simon Miller , Christian Wagner , Uwe Aickelin , Jonathan M. Garibaldi

We introduce two kinds of risk measures with respect to some reference probability measure, which both allow for a certain order structure and domination property. Analyzing their relation to each other leads to the question when a certain…

Risk Management · Quantitative Finance 2022-04-15 Christa Cuchiero , Guido Gazzani , Irene Klein

Systemic risk measures have been shown to be predictive of financial crises and declines in real activity. Thus, forecasting them is of major importance in finance and economics. In this paper, we propose a new forecasting method for…

Methodology · Statistics 2025-04-23 Yannick Hoga

We study a general risk measure called the generalized shortfall risk measure, which was first introduced in Mao and Cai (2018). It is proposed under the rank-dependent expected utility framework, or equivalently induced from the cumulative…

Risk Management · Quantitative Finance 2024-11-12 Tiantian Mao , Gilles Stupfler , Fan Yang

The work deals with the risk assessment theory. An unitary risk algorithm is elaborated. The algorithm is based on parallel curves. The basic curve of risk is a hyperbolic curve, obtained as a multiplication between the probability of…

Risk Management · Quantitative Finance 2013-03-08 Nicolae Popoviciu , Floarea Baicu

Utilizing established risk factors and prognostic models can often improve the construction of a newer risk model that uses novel biomarkers in a smaller, internal study. However, directly borrowing information from an established…

Methodology · Statistics 2026-03-12 Nicholas C. Henderson

The paper provides an overview of the theory and applications of risk-sensitive Markov decision processes. The term 'risk-sensitive' refers here to the use of the Optimized Certainty Equivalent as a means to measure expectation and risk.…

Risk Management · Quantitative Finance 2025-09-23 Nicole Bäuerle , Anna Jaśkiewicz
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