Cover Image

The Risk Quadrangle in Optimization: An Overview with Recent Results and Extensions

Fuente: arXiv

Saved in:

Bibliographic Details
Main Authors:	Grechuk, Bogdan, Malandii, Anton, Rockafellar, Terry, Uryasev, Stan
Format:	Preprint
Published:	2026
Subjects:	Optimization and Control Probability Statistics Theory Risk Management Machine Learning
Online Access:	Acceder al recurso
Tags:	Add Tag No Tags, Be the first to tag this record!

Similar Items

Biased Mean Quadrangle and Applications
by: Malandii, Anton, et al.
Published: (2026)

Support Vector Regression: Risk Quadrangle Framework
by: Malandii, Anton, et al.
Published: (2022)

Risk Quadrangle and Robust Optimization Based on Extended $φ$-Divergence
by: Peng, Cheng, et al.
Published: (2024)

A Martingale approach to continuous Portfolio Optimization under CVaR like constraints
by: Lelong, Jérôme, et al.
Published: (2025)

Optimal Risk-Sharing Rules in Network-based Decentralized Insurance
by: Fogarty, Heather N., et al.
Published: (2026)

The Scaling Behaviors in Achieving High Reliability via Chance-Constrained Optimization
by: Deo, Anand, et al.
Published: (2025)

Solving The Dynamic Volatility Fitting Problem: A Deep Reinforcement Learning Approach
by: Gnabeyeu, Emmanuel, et al.
Published: (2024)

Decomposition Pipeline for Large-Scale Portfolio Optimization with Applications to Near-Term Quantum Computing
by: Acharya, Atithi, et al.
Published: (2024)

Optimal dividend and capital injection under self-exciting claims
by: Aubert, Paulin, et al.
Published: (2025)

Singular Control in Inventory Management with Smooth Ambiguity
by: Archankul, Arnon, et al.
Published: (2025)

Optimal Cash Transfers and Microinsurance to Reduce Social Protection Costs
by: Azcue, Pablo, et al.
Published: (2025)

Estimation of Systemic Shortfall Risk Measure using Stochastic Algorithms
by: Kaakai, Sarah, et al.
Published: (2022)

Generative Adversarial Regression (GAR): Learning Conditional Risk Scenarios
by: Asadi, Saeed, et al.
Published: (2026)

Conditional Risk Minimization with Side Information: A Tractable, Universal Optimal Transport Framework
by: Xie, Xinqiao, et al.
Published: (2025)

Risk-Sensitive Mean Field Games with Common Noise: A Theoretical Study with Applications to Interbank Markets
by: Ren, Xin Yue, et al.
Published: (2024)

LQG Risk-Sensitive Single-Agent and Major-Minor Mean-Field Game Systems: A Variational Framework
by: Liu, Hanchao, et al.
Published: (2023)

Risk Aware Benchmarking of Large Language Models
by: Nitsure, Apoorva, et al.
Published: (2023)

Convolution Bounds on Quantile Aggregation
by: Blanchet, Jose, et al.
Published: (2020)

Robust Hedging of path-dependent options using a min-max algorithm
by: Banerjee, Purba, et al.
Published: (2025)

On the Impact of Feeding Cost Risk in Aquaculture Valuation and Decision Making
by: Ewald, Christian Oliver, et al.
Published: (2023)

Multidimensional indefinite stochastic Riccati equations and zero-sum stochastic linear-quadratic differential games with non-Markovian regime switching
by: Zhang, Panpan, et al.
Published: (2023)

Sampler-Robust Optimization under Generative Models
by: Zhang, Ziwei, et al.
Published: (2026)

The Boosted Difference of Convex Functions Algorithm for Value-at-Risk Constrained Portfolio Optimization
by: Thormann, Marah-Lisanne, et al.
Published: (2024)

Optimal nonparametric estimation of the expected shortfall risk
by: Bartl, Daniel, et al.
Published: (2024)

Arbitrage-free catastrophe reinsurance valuation for compound dynamic contagion claims
by: Jang, Jiwook, et al.
Published: (2025)

Generalized Orlicz premia
by: Aygün, Mücahit, et al.
Published: (2025)

Community detection by simulated bifurcation
by: Li, Wei, et al.
Published: (2024)

Fast Spawn\&Prune (FS\&P): Global convergence of stochastic conic particle gradient descent via birth/death process
by: De Castro, Yohann, et al.
Published: (2026)

Statistical Inference for Linear Functionals of Online SGD in High-dimensional Linear Regression
by: Agrawalla, Bhavya, et al.
Published: (2023)

High-dimensional scaling limits and fluctuations of online least-squares SGD with smooth covariance
by: Balasubramanian, Krishnakumar, et al.
Published: (2023)

Optimal and instance-dependent guarantees for Markovian linear stochastic approximation
by: Mou, Wenlong, et al.
Published: (2021)

A Piecewise Lyapunov Analysis of Sub-quadratic SGD: Applications to Robust and Quantile Regression
by: Zhang, Yixuan, et al.
Published: (2025)

Convergence of coordinate ascent variational inference for log-concave measures via optimal transport
by: Arnese, Manuel, et al.
Published: (2024)

Alternating minimization for generalized rank one matrix sensing: Sharp predictions from a random initialization
by: Chandrasekher, Kabir Aladin, et al.
Published: (2022)

4+3 Phases of Compute-Optimal Neural Scaling Laws
by: Paquette, Elliot, et al.
Published: (2024)

Early Stopping in Contextual Bandits and Inferences
by: Cui, Zihan
Published: (2025)

Orlicz regrets to consistently bound statistics of random variables with an application to environmental indicators
by: Yoshioka, Hidekazu, et al.
Published: (2023)

Statistical guarantees for continuous-time policy evaluation: blessing of ellipticity and new tradeoffs
by: Mou, Wenlong
Published: (2025)

Is RL fine-tuning harder than regression? A PDE learning approach for diffusion models
by: Mou, Wenlong
Published: (2025)

A Rank-Dependent Theory for Decision under Risk and Ambiguity
by: Laeven, Roger J. A., et al.
Published: (2023)