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Value-at-Risk (VaR) is an institutional measure of risk favored by financial regulators. VaR may be interpreted as a quantile of future portfolio values conditional on the information available, where the most common quantile used is 95%.…

Risk Management · Quantitative Finance 2016-05-18 Khizar Qureshi

Accurate computation of robust estimates for extremal quantiles of empirical distributions is an essential task for a wide range of applicative fields, including economic policymaking and the financial industry. Such estimates are…

Methodology · Statistics 2024-11-04 Pietro Bogani , Matteo Fontana , Luca Neri , Simone Vantini

The increasing value of data held in enterprises makes it an attractive target to attackers. The increasing likelihood and impact of a cyber attack have highlighted the importance of effective cyber risk estimation. We propose two methods…

Cryptography and Security · Computer Science 2021-04-23 Raisa Dzhamtyrova , Carsten Maple

Risk measures are important key figures to measure the adequacy of the reserves of a company. The most common risk measures in practice are Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR). Recently, quantum-based algorithms are…

Quantum Physics · Physics 2025-01-29 Christian Laudagé , Ivica Turkalj

A new realized conditional autoregressive Value-at-Risk (VaR) framework is proposed, through incorporating a measurement equation into the original quantile regression model. The framework is further extended by employing various Expected…

Risk Management · Quantitative Finance 2021-01-18 Chao Wang , Richard Gerlach , Qian Chen

Value-at-risk (VaR) has been playing the role of a standard risk measure since its introduction. In practice, the delta-normal approach is usually adopted to approximate the VaR of portfolios with option positions. Its effectiveness,…

Methodology · Statistics 2019-04-22 Junyao Chen , Tony Sit , Hoi Ying Wong

Conditional Value-at-Risk (CVaR) is a leading tail-risk measure in finance, central to both regulatory and portfolio optimization frameworks. Classical estimation of CVaR and its gradients relies on Monte Carlo simulation, incurring…

Quantum Physics · Physics 2026-05-19 Vasilis Skarlatos , Nikos Konofaos

In economics, insurance and finance, value at risk (VaR) is a widely used measure of the risk of loss on a specific portfolio of financial assets. For a given portfolio, time horizon, and probability $\alpha$, the $100\alpha\%$ VaR is…

Risk Management · Quantitative Finance 2018-03-15 Raúl Torres , Rosa E. Lillo , Henry Laniado

Value at Risk (VaR) is a quantitative measure used to evaluate the risk linked to the potential loss of investment or capital. Estimation of the VaR entails the quantification of prospective losses in a portfolio of investments, using a…

Mathematical Finance · Quantitative Finance 2024-10-01 Minglian Lin , Indranil SenGupta , William Wilson

We consider an online stochastic game with risk-averse agents whose goal is to learn optimal decisions that minimize the risk of incurring significantly high costs. Specifically, we use the Conditional Value at Risk (CVaR) as a risk measure…

Machine Learning · Computer Science 2022-06-17 Zifan Wang , Yi Shen , Michael M. Zavlanos

In safety-critical decision-making, the environment may evolve over time, and the learner adjusts its risk level accordingly. This work investigates risk-averse online optimization in dynamic environments with varying risk levels, employing…

Optimization and Control · Mathematics 2025-12-30 Siyi Wang , Zifan Wang , Karl H. Johansson

Conditional Value at Risk (CVaR) is a prominent risk measure that is being used extensively in various domains. We develop a new formula for the gradient of the CVaR in the form of a conditional expectation. Based on this formula, we…

Machine Learning · Statistics 2014-11-25 Aviv Tamar , Yonatan Glassner , Shie Mannor

We introduce a semiparametric approach for forecasting Value-at-Risk (VaR) and Expected Shortfall (ES) by modeling the conditional scale of financial returns, defined as the difference between two specified quantiles, via restricted…

Econometrics · Economics 2026-03-18 Xiaochun Liu , Richard Luger

A method for quantile-based, semi-parametric historical simulation estimation of multiple step ahead Value-at-Risk (VaR) and Expected Shortfall (ES) models is developed. It uses the quantile loss function, analogous to how the…

Statistical Finance · Quantitative Finance 2025-03-06 Richard Gerlach , Antonio Naimoli , Giuseppe Storti

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…

Optimization and Control · Mathematics 2016-08-03 Helin Zhu , Joshua Hale , Enlu Zhou

Distributional reinforcement learning (RL) -- in which agents learn about all the possible long-term consequences of their actions, and not just the expected value -- is of great recent interest. One of the most important affordances of a…

Artificial Intelligence · Computer Science 2021-11-15 Chris Gagne , Peter Dayan

Considering non-stationary environments in online optimization enables decision-maker to effectively adapt to changes and improve its performance over time. In such cases, it is favorable to adopt a strategy that minimizes the negative…

Systems and Control · Electrical Eng. & Systems 2024-04-05 Siyi Wang , Zifan Wang , Xinlei Yi , Michael M. Zavlanos , Karl H. Johansson , Sandra Hirche

Value at Risk (VaR) and stress testing are two of the most widely used approaches in portfolio risk management to estimate potential market value losses under adverse market moves. VaR quantifies potential loss in value over a specified…

Computational Finance · Quantitative Finance 2024-10-01 Krishan Mohan Nagpal

We propose a new approach, termed Realized Risk Measures (RRM), to estimate Value-at-Risk (VaR) and Expected Shortfall (ES) using high-frequency financial data. It extends the Realized Quantile (RQ) approach proposed by Dimitriadis and…

Risk Management · Quantitative Finance 2025-10-21 Federico Gatta , Fabrizio Lillo , Piero Mazzarisi

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…

Risk Management · Quantitative Finance 2025-07-21 Abiodun Finbarrs Oketunji
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