arXiv subjects

Qianwen Zhu

Publications and source records attributed to Qianwen Zhu.

3 recordsLinked to original sources

arXiv2026

Reliable Real-Time Value at Risk Estimation via Quantile Regression Forest with Conformal Calibration

Rapidly evolving market conditions call for real-time risk monitoring, but its online estimation remains challenging. In this paper, we study the online estimation of one of the most widely used risk measures, Value at Risk (VaR). Its accurate and reliable estimation is essential for timely risk control and informed decision-making. We propose to use the quantile regression forest in the offline-simulation-online-estimation (OSOA) framework. Specifically, the quantile regression forest is trained offline to learn the relationship between the online VaR and risk factors, and real-time VaR estimates are then produced online by incorporating observed risk factors. To further ensure reliability, we develop a conformalized estimator that calibrates the online VaR estimates. To the best of our knowledge, we are the first to leverage conformal calibration to estimate real-time VaR reliably based on the OSOA formulation. Theoretical analysis establishes the consistency and coverage validity of the proposed estimators. Numerical experiments confirm the proposed method and demonstrate its effectiveness in practice.

stat.ML↗

arXiv2025

Extending structures for pre-Poisson algebras and pre-Poisson bialgebras

In this paper, we explore the extending structures problem by the unified product for pre-Poisson algebras. In particular, the crossed product and the factorization problem are investigated. Furthermore, a special case of extending structures is studied under the case of pre-Poisson algebras, which leads to the discussion of bicrossed products and matched pairs of pre-Poisson algebras. We develop a bialgebra theory for pre-Poisson algebras and establish the equivalence between matched pairs and pre-Poisson bialgebras. We study coboundary pre-Poisson bialgebras, which lead to the introduction of the pre-Poisson Yang-Baxter equation (PPYBE). A symmetric solution of the PPYBE naturally gives a coboundary pre-Poisson bialgebra.

math.RA↗

arXiv2024

Non-abelian extensions of relative Rota-Baxter Lie algebras and Wells type exact sequences

In this paper, we explore non-abelian extensions of relative Rota-Baxter Lie algebras and classify the non-abelian extensions by introducing the non-abelian second cohomology group. We also study the inducibility of a pair of automorphisms about a non-abelian extension of relative Rota-Baxter Lie algebras and derive the Wells type exact sequences. Finally, we investigate the inducibility problem of pairs of derivations about an abelian extension of relative Rota-Baxter Lie algebras and give an exact sequence of Wells type.

math.RA↗