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Model uncertainty is a crucial issue in statistics, econometrics and machine learning, yet its definition remains ambiguous and is subject to various interpretations in the literature. So far, there has not been a universally accepted…

Methodology · Statistics 2025-08-12 Guangyuan Cui , Yuting Wei , Xinyu Zhang

This paper deals with three major types of convergence of probability measures on metric spaces: weak convergence, setwise converges, and convergence in the total variation. First, it describes and compares necessary and sufficient…

Probability · Mathematics 2014-07-04 Eugene A. Feinberg , Pavlo O. Kasyanov , Michael Z. Zgurovsky

Risk assessment under different possible scenarios is a source of uncertainty that may lead to concerning financial losses. We address this issue, first, by adapting a robust framework to the class of spectral risk measures. Second, we…

Risk Management · Quantitative Finance 2019-05-21 Mohammed Berkhouch , Ghizlane Lakhnati , Marcelo Brutti Righi

Machine Learning is a diverse field applied across various domains such as computer science, social sciences, medicine, chemistry, and finance. This diversity results in varied evaluation approaches, making it difficult to compare models…

Machine Learning · Computer Science 2025-07-08 Silvia Beddar-Wiesing , Alice Moallemy-Oureh , Marie Kempkes , Josephine M. Thomas

This article is part of a comprehensive research project on liquidity risk in asset management, which can be divided into three dimensions. The first dimension covers liability liquidity risk (or funding liquidity) modeling, the second…

Risk Management · Quantitative Finance 2021-05-19 Thierry Roncalli , Amina Cherief , Fatma Karray-Meziou , Margaux Regnault

Conditional forecasts of risk measures play an important role in internal risk management of financial institutions as well as in regulatory capital calculations. In order to assess forecasting performance of a risk measurement procedure,…

Risk Management · Quantitative Finance 2017-02-22 Natalia Nolde , Johanna F. Ziegel

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

Model risk in credit portfolio models is a serious issue for banks but has so far not been tackled comprehensively. We will demonstrate how to deal with uncertainty in all model parameters in an all-embracing, yet easy-to-implement way.

Risk Management · Quantitative Finance 2021-11-30 Christian Meyer

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

This chapter makes a review, in a complete methodological framework, of various global sensitivity analysis methods of model output. Numerous statistical and probabilistic tools (regression, smoothing, tests, statistical learning, Monte…

Statistics Theory · Mathematics 2014-04-10 Bertrand Iooss , Paul Lemaître

In this research, starting from a widely accepted definition of risk, we support the idea that risk reduction is a more realistic objective than risk minimization, which represents a theoretical utopia. Furthermore, significant risk…

Risk Management · Quantitative Finance 2026-05-01 Pierpaolo Uberti

We propose a decision-analytical approach to comparing the flexibility of decision situations from the perspective of a decision-maker who exhibits constant risk-aversion over a monetary value model. Our approach is simple yet seems to be…

Artificial Intelligence · Computer Science 2013-02-18 Ross D. Shachter , Marvin Mandelbaum

This paper enhances the pricing of derivatives as well as optimal control problems to a level comprising risk. We employ nested risk measures to quantify risk, investigate the limiting behavior of nested risk measures within the classical…

Mathematical Finance · Quantitative Finance 2021-02-16 Alois Pichler , Ruben Schlotter

This paper examines the precision of estimators of Quantile-Based Risk Measures (Value at Risk, Expected Shortfall, Spectral Risk Measures). It first addresses the question of how to estimate the precision of these estimators, and proposes…

Risk Management · Quantitative Finance 2011-03-30 Kevin Dowd , John Cotter

We show how risk measures originally defined in a model free framework in terms of acceptance sets and reference assets imply a meaningful underlying probability structure. Hereafter we construct a maximal domain of definition of the risk…

Risk Management · Quantitative Finance 2017-11-27 Felix-Benedikt Liebrich , Gregor Svindland

Starting from the requirement that risk measures of financial portfolios should be based on their losses, not their gains, we define the notion of loss-based risk measure and study the properties of this class of risk measures. We…

Risk Management · Quantitative Finance 2014-03-26 Rama Cont , Romain Deguest , Xuedong He

The estimation of risk measures recently gained a lot of attention, partly because of the backtesting issues of expected shortfall related to elicitability. In this work we shed a new and fundamental light on optimal estimation procedures…

Risk Management · Quantitative Finance 2017-08-25 Marcin Pitera , Thorsten Schmidt

Risk management often plays an important role in decision making under uncertainty. In quantitative risk management, assessing and optimizing risk metrics requires efficient computing techniques and reliable theoretical guarantees. In this…

Optimization and Control · Mathematics 2026-01-01 Zhaolin Hu

Endowing robots with the capability of assessing risk and making risk-aware decisions is widely considered a key step toward ensuring safety for robots operating under uncertainty. But, how should a robot quantify risk? A natural and common…

Robotics · Computer Science 2017-11-02 Anirudha Majumdar , Marco Pavone