Zhijian He
South China University of Technology
Dr. Zhijian He is an associate Professor at School of Mathematics of South China University of Technology (SCUT). Before joining SCUT, he obtained a Ph.D. in Statistics from Department of Mathematical Science of Tsinghua University, advised by Prof. Xiaoqun Wang. His research interests are quasi-Monte Carlo methods and their applications in quantitative finance and statistics. He was a silver prize recipient of the New World Mathematics Awards (NWMA). He has published in top journals in the fields of statistics and computational mathematics, such as Journal of the Royal Statistical Society: Series B, SIAM Journal on Numerical Analysis, SIAM Journal on Scientific Computing, Mathematics of Computation. Part of his research is supported by National Science Foundation of China (NSFC).
Computational Statistics
Computational Finance
Monte Carlo and quasi-Monte methods
PhD in Statistics, 2015
BSc in Mathematics and Applied Mathematics, 2010
Jan 2018 – Present Guangzhou
Taught Mathematical Statistics, Advanced Statistics etc.
Sun Yat-Sen University
Jan 2016 – Dec 2018 Guangzhou
Sep 2015 – Dec 2015 Guangzhou
Writing technical content in Academic
Academic is designed to give technical content creators a seamless experience. You can focus on the content and Academic handles the rest. Highlight your code snippets, take notes on math classes, and draw diagrams from textual representation.
Display Jupyter Notebooks with Academic
Learn how to blog in Academic using Jupyter notebooks
Last updated on Sep 5, 2019 2 min read
Academic: the website builder for Hugo
Create a beautifully simple website in under 10 minutes.
Zhijian He, 吳恩達
Last updated on Apr 17, 2019 3 min read Demo, 教程
Hello R Markdown
R Markdown This is an R Markdown document. Markdown is a simple formatting syntax for authoring HTML, PDF, and MS Word documents. For more details on using R Markdown see http://rmarkdown.
Jul 23, 2015 1 min read R
All Deep Learning Other
External Project
An example of linking directly to an external project website using external_link.
Internal Project
An example of using the in-built project page.
Recent & Upcoming Talks
Example Talk
An example talk using Academic's Markdown slides feature.
Jun 1, 2030 1:00 PM — 3:00 PM Source Themes HQ
Project Slides Follow
贝叶斯计算及其挑战
Sep 2, 2020 7:00 PM — 9:00 PM 四号楼4135
PDF Project Follow
September 2019 SIAM Journal on Numerical Analysis, 57(2), 854-874
On the Error Rate of Conditional Quasi-Monte Carlo for Discontinuous Functions
This paper studies the rate of convergence for conditional quasi–Monte Carlo (QMC), which is a counterpart of conditional Monte Carlo. We focus on discontinuous integrands defined on the whole of $\mathbb{R}^d$, which can be unbounded. Under suitable conditions, we show that conditional QMC not only has the smoothing effect (up to infinitely times differentiable) but also can bring orders of magnitude reduction in integration error compared to plain QMC. Particularly, for some typical problems in options pricing and Greeks estimation, conditional randomized QMC that uses $n$ samples yields a mean error of $O(n^{-1+\epsilon})$ for arbitrarily small $\epsilon>0$. As a byproduct, we find that this rate also applies to randomized QMC integration with all terms of the analysis of variance decomposition of the discontinuous integrand, except the one of highest order.
Slides DOI
February 2018 Mathematics of Computation, 87(314), 2857-2870
Quasi-Monte Carlo for Discontinuous Integrands with Singularities along the Boundary of the Unit Cube
This paper studies randomized quasi-Monte Carlo (QMC) sampling for discontinuous integrands having singularities along the boundary of the unit cube $ [0,1]^d$. Both discontinuities and singularities are extremely common in the pricing and hedging of financial derivatives and have a tremendous impact on the accuracy of QMC. It was previously known that the root mean square error of randomized QMC is only $ o(n^{1/2})$ for discontinuous functions with singularities. We find that under some mild conditions, randomized QMC yields an expected error of $ O(n^{-1/2-1/(4d-2)+\epsilon })$ for arbitrarily small $ \epsilon >0$. Moreover, one can get a better rate if the boundary of discontinuities is parallel to some coordinate axes. As a by-product, we find that the expected error rate attains $ O(n^{-1+\epsilon })$ if the discontinuities are QMC-friendly, in the sense that all the discontinuity boundaries are parallel to coordinate axes. The results can be used to assess the QMC accuracy for some typical problems from financial engineering.
Zhijian He, Art Owen
March 2016 Journal of the Royal Statistical Society: Series B, 78(4), 917-931
Extensible Grids -- Uniform Sampling on a Space-Filling Curve
We study the properties of points in $[0,1]^d$ generated by applying Hilbert's space-filling curve to uniformly distributed points in $[0,1]$. For deterministic sampling we obtain a discrepancy of $O(n^{-1/d})$ for $d\ge2$. For random stratified sampling, and scrambled van der Corput points, we get a mean squared error of $O(n^{-1-2/d})$ for integration of Lipschitz continuous integrands, when $d\ge3$. These rates are the same as one gets by sampling on $d$ dimensional grids and they show a deterioration with increasing $d$. The rate for Lipschitz functions is however best possible at that level of smoothness and is better than plain IID sampling. Unlike grids, space-filling curve sampling provides points at any desired sample size, and the van der Corput version is extensible in $n$. We also introduce a class of piecewise Lipschitz functions whose discontinuities are in rectifiable sets described via Minkowski content. Although these functions may have infinite variation in the sense of Hardy and Krause, they can be integrated with a mean squared error of $O(n^{-1-1/d})$. It was previously known only that the rate was $o(n^{-1})$. Other space-filling curves, such as those due to Sierpinski and Peano, also attain these rates, while upper bounds for the Lebesgue curve are somewhat worse, as if the dimension were $\log_2(3)$ times as high.
Quickly discover relevant content by filtering publications.
Convergence analysis of quasi-Monte Carlo sampling for quantile and expected shortfall
Quantiles and expected shortfalls are usually used to measure risks of stochastic systems, which are often estimated by Monte Carlo …
Zhijian He, Xiaoqun Wang
An Integrated Quasi-Monte Carlo Method for Handling High Dimensional Problems with Discontinuities in Financial Engineering
Quasi-Monte Carlo (QMC) method is a useful numerical tool for pricing and hedging of complex financial derivatives. These problems are …
This paper studies the rate of convergence for conditional quasi–Monte Carlo (QMC), which is a counterpart of conditional Monte …
An importance sampling-based smoothing approach for quasi-Monte Carlo simulation of discrete barrier options
Handling discontinuities in financial engineering is a challenging task when using quasi-Monte Carlo (QMC) method. This paper develops …
Fei Xie, Zhijian He(?), Xiaoqun Wang
Asymptotic normality of extensible grid sampling
Recently, He and Owen (J R Stat Soc Ser B 78(4):917–931, 2016) proposed the use of Hilbert's space filling curve (HSFC) in numerical …
Zhijian He, Lingjiong Zhu
Academic Deep Learning Demo Finance plot QMC R Markdown regression 开源
hezhijian@scut.edu.cn
华南理工大学四号楼4301, 广州, 广东省 510640
Privacy Policy · Terms
Zhijian He 2020