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Model checking and testing are two areas with a similar goal: to verify that a system satisfies a property. They start with different hypothesis on the systems and develop many techniques with different notions of approximation, when an…

Logic in Computer Science · Computer Science 2013-04-19 M. C. Gaudel , R. Lassaigne , F. Magniez , M. de Rougemont

Volatility is the canonical measure of financial risk, a role largely inherited from Modern Portfolio Theory. Yet, its universality rests on restrictive efficiency assumptions that render volatility, at best, an incomplete proxy for true…

Mathematical Finance · Quantitative Finance 2026-05-01 Sergio Bianchi , Daniele Angelini

We pick up the regime switching model for asset returns introduced by Rogers and Zhang. The calibration involves various markets including implied volatility in order to gain additional predictive power. We focus on the calculation of risk…

Risk Management · Quantitative Finance 2012-12-18 Rainer Haidinger , Richard Warnung

We propose a novel strategy for multivariate extreme value index estimation. In applications such as finance, volatility and risk present in the components of a multivariate time series are often driven by the same underlying factors, such…

Statistics Theory · Mathematics 2020-03-24 Joni Virta , Niko Lietzén , Lauri Viitasaari , Pauliina Ilmonen

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…

Risk Management · Quantitative Finance 2024-11-15 Tong Pu , Yunran Wei , Yiying Zhang

Expanding on techniques of concentration of measure, we develop a quantitative framework for modeling liquidity risk using convex risk measures. The fundamental objects of study are curves of the form $(\rho(\lambda X))_{\lambda \ge 0}$,…

Risk Management · Quantitative Finance 2015-10-28 Daniel Lacker

Systemic risk measures are crucial for the stability of financial markets, yet classical formulations fail to capture the complexity of market volatility. We propose a new framework for systemic risk measurement on the variable-exponent…

Risk Management · Quantitative Finance 2026-02-25 Fei Sun , Jieming Zhou

Machine learning models are often used to inform real world risk assessment tasks: predicting consumer default risk, predicting whether a person suffers from a serious illness, or predicting a person's risk to appear in court. Given…

Machine Learning · Computer Science 2023-06-27 Jamelle Watson-Daniels , David C. Parkes , Berk Ustun

In the present paper we study quantile risk measures and their domain. Our starting point is that, for a probability measure $ Q $ on the open unit interval and a wide class $ \mathcal{L}_Q $ of random variables, we define the quantile risk…

Probability · Mathematics 2017-07-24 Sebastian Fuchs , Ruben Schlotter , Klaus D. Schmidt

Estimating the covariance of asset returns, i.e., the risk model, is a key component of financial portfolio construction and evaluation. Most risk modeling approaches produce a factor model that decomposes the asset variability into two…

Quantile regression is a powerful tool for detecting exposure-outcome associations given covariates across different parts of the outcome's distribution, but has two major limitations when the aim is to infer the effect of an exposure.…

The need for control strategies that can address dynamic system uncertainty is becoming increasingly important. In this work, we propose a Model Predictive Control by quantifying the risk of failure in our system model. The proposed control…

Systems and Control · Electrical Eng. & Systems 2023-02-17 Mostafa Tavakkoli Anbarani , Efe C. Balta , Rômulo Meira-Góes , Ilya Kovalenko

In this paper, we are interested in evaluating the resilience of financial portfolios under extreme economic conditions. Therefore, we use empirical measures to characterize the transmission process of macroeconomic shocks to risk…

Applications · Statistics 2019-05-21 Helder Rojas , David Dias

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…

Mathematical Finance · Quantitative Finance 2015-04-27 Francesca Biagini , Jean-Pierre Fouque , Marco Frittelli , Thilo Meyer-Brandis

We introduce a general decision tree framework to value an option to invest/divest in a project, focusing on the model risk inherent in the assumptions made by standard real option valuation methods. We examine how real option values depend…

General Finance · Quantitative Finance 2018-09-06 Carol Alexander , Xi Chen

We introduce the concept of partial law invariance, generalizing the concepts of law invariance and probabilistic sophistication widely used in decision theory, as well as statistical and financial applications. This new concept is…

Risk Management · Quantitative Finance 2025-06-24 Yi Shen , Zachary Van Oosten , Ruodu Wang

This paper is the continuation of "Pricing with coherent risk" and deals with further applications of coherent risk measures to problems of finance. First, we study the optimization problem. Three forms of this problem are considered.…

Probability · Mathematics 2008-12-10 Alexander S. Cherny

The risk of extreme environmental events is of great importance for both the authorities and the insurance industry. This paper concerns risk measures in a spatial setting, in order to introduce the spatial features of damages stemming from…

Probability · Mathematics 2016-10-12 Erwan Koch

We present an historical overview about the connections between the analysis of risk and the control of autonomous systems. We offer two main contributions. Our first contribution is to propose three overlapping paradigms to classify the…

Artificial Intelligence · Computer Science 2022-07-13 Yuheng Wang , Margaret P. Chapman

Proper quantification of predictive uncertainty is essential for the use of machine learning in safety-critical applications. Various uncertainty measures have been proposed for this purpose, typically claiming superiority over other…

Machine Learning · Computer Science 2025-12-16 Paul Hofman , Yusuf Sale , Eyke Hüllermeier