arXiv subjects

Weihuan Huang

Publications and source records attributed to Weihuan Huang.

6 recordsLinked to original sources

arXiv2026

Staffing under Taylor's Law: A Unifying Framework for Bridging Square-root and Linear Safety Rules

Staffing rules are an essential management tool in service industries for meeting target service levels. The square-root safety rule, based on the Poisson arrival assumption, has been commonly used. However, empirical findings suggest that arrivals often exhibit ``over-dispersion'', meaning that the variance exceeds the mean. In this paper, we develop a new doubly stochastic Poisson process model that captures two key features of over-dispersed arrivals: (i) Taylor's law, which links the variance to the mean through a power-law relationship, and (ii) temporal correlation decay, where the correlation between arrival counts in disjoint time intervals decreases as the time gap grows. Using this model, we study how over-dispersion affects staffing and derive a closed-form staffing formula to ensure a desired service level. Our formula shows that the safety level grows as a power of the nominal load. The exponent lies between 1/2 (the square-root safety rule) and 1 (the linear safety rule). It depends on the degree of over-dispersion, and it implies that Taylor's law is the dominant factor in determining staffing levels in heavy traffic. Extensive numerical experiments with both simulated and real arrival data show that our model and staffing rules significantly outperform various alternatives.

math.PR↗

arXiv2025

Boosting Accelerated Proximal Gradient Method with Adaptive Sampling for Stochastic Composite Optimization

We develop an adaptive Nesterov accelerated proximal gradient (adaNAPG) algorithm for stochastic composite optimization problems, boosting the Nesterov accelerated proximal gradient (NAPG) algorithm through the integration of an adaptive sampling strategy for gradient estimation. We provide a complexity analysis demonstrating that the new algorithm, adaNAPG, achieves both the optimal iteration complexity and the optimal sample complexity as outlined in the existing literature. Additionally, we establish a central limit theorem for the iteration sequence of the new algorithm adaNAPG, elucidating its convergence rate and efficiency.

math.OC↗

arXiv2023

Estimating Systemic Risk within Financial Networks: A Two-Step Nonparametric Method

CoVaR (conditional value-at-risk) is a crucial measure for assessing financial systemic risk, which is defined as a conditional quantile of a random variable, conditioned on other random variables reaching specific quantiles. It enables the measurement of risk associated with a particular node in financial networks, taking into account the simultaneous influence of risks from multiple correlated nodes. However, estimating CoVaR presents challenges due to the unobservability of the multivariate-quantiles condition. To address the challenges, we propose a two-step nonparametric estimation approach based on Monte-Carlo simulation data. In the first step, we estimate the unobservable multivariate-quantiles using order statistics. In the second step, we employ a kernel method to estimate the conditional quantile conditional on the order statistics. We establish the consistency and asymptotic normality of the two-step estimator, along with a bandwidth selection method. The results demonstrate that, under a mild restriction on the bandwidth, the estimation error arising from the first step can be ignored. Consequently, the asymptotic results depend solely on the estimation error of the second step, as if the multivariate-quantiles in the condition were observable. Numerical experiments demonstrate the favorable performance of the two-step estimator.

q-fin.RM↗

arXiv2022

Monte-Carlo Estimation of CoVaR

${\rm CoVaR}$ is one of the most important measures of financial systemic risks. It is defined as the risk of a financial portfolio conditional on another financial portfolio being at risk. In this paper we first develop a Monte-Carlo simulation-based batching estimator of CoVaR and study its consistency and asymptotic normality. We show that the optimal rate of convergence of the batching estimator is $n^{-1/3}$, where $n$ is the sample size. We then develop an importance-sampling inspired estimator under the delta-gamma approximations to the portfolio losses, and we show that the rate of convergence of the estimator is $n^{-1/2}$. Numerical experiments support our theoretical findings and show that both estimators work well.

q-fin.RM↗

arXiv2018

On Independence for Capacities to Fit Ellsberg's Model with a Weak Law of Large Numbers

This paper introduces new notions of Fubini independence and Exponential independence of random variables under capacities to fit Ellsberg's model, and finds out the relations between Fubini independence, Exponential independence, MacCheroni and Marinacci's independence and Peng's independence. As an application, we give a weak law of large numbers for capacities under Exponential independence. Simulations show that Ellsberg's model enjoy the weak law of large numbers when there is mean uncertainty with or without variance uncertainty.

math.PR↗

arXiv2018

Almost Sure Central Limit Theorem in Sub-linear Expectation Spaces

Peng (2006) initiated a new kind of central limit theorem under sub-linear expectations. Song (2017) gave an estimate of the rate of convergence of Peng's central limit theorem. Based on these results, we establish a new kind of almost sure central limit theorem under sub-linear expectations in this paper, which is a quasi sure convergence version of Peng's central limit theorem. Moreover, this result is a natural extension of the classical almost sure central limit theorem to the case where the probability is no longer additive. Meanwhile, we prove a new kind of strong law of large numbers for non-additive probabilities without the independent identically distributed assumption.

math.PR↗