Guo Liang

Du-Yi Wang, Guo Liang, Kun Zhang et al.

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.

Guo Liang, Guangwu Liu, Kun Zhang

Finite difference (FD) approximation is a classic approach to stochastic gradient estimation when only noisy function realizations are available. In this paper, we first provide a sample-driven method via the bootstrap technique to estimate the optimal perturbation, and then propose an efficient FD estimator based on correlated samples at the estimated optimal perturbation. Furthermore, theoretical analyses of both the perturbation estimator and the FD estimator reveal that, {\it surprisingly}, the correlation enables the proposed FD estimator to achieve a reduction in variance and, in some cases, a decrease in bias compared to the traditional optimal FD estimator. Numerical results confirm the efficiency of our estimators and align well with the theory presented, especially in scenarios with small sample sizes. Finally, we apply the estimator to solve derivative-free optimization (DFO) problems, and numerical studies show that DFO problems with 100 dimensions can be effectively solved.