LI, Yutian
Assistant Professor

Education Background
PhD（City University of Hong Kong）
B.Sc.（Jilin University）

Research Field
Analysis and application, partial differential equations, scientific calculations and numerical analysis, mathematical finance
Email
liyutian@cuhk.edu.cn
Biography
Prof. LI Yutian received his B.Sc. degree in Mathematics and Applied Mathematics from Jilin University in 2005, and the MPhil and PhD degrees in Mathematics both from City University of Hong Kong in 2007 and 2010 respectively. He was a Postdoc Research Fellow at Liu Bie Ju Centre for Mathematical Sciences of City University of Hong Kong from 2010 to 2012. He then worked at Hong Kong Baptist University as a Research Assistant Professor from 2012 to 2017. He Joined the School of Science and Engineering of Chinese University of Hong Kong, Shenzhen as an Assistant Professor in December 2017.
Prof. Li’s research interests include: Partial differential equations, Applied analysis, Scientific computing, Mathematical finances. He has published more than 20 papers in recognized journals in mathematics, applied mathematics, engineering and finance, including:
Studies in Applied Mathematics, Applied Mathematical Letters, Analysis and Applications, Constructive Approximations, Proceedings of the Royal Society London A, Discrete and Continuous Dynamical Systems, Journal of Scientific Computing, Optics Expresses, IEEE Transaction on Microwave Theory and Technologies, Quantitative Finance, etc.

Academic Publications
Applied Analysis
Yutian Li, Saiyu Liu, Shuaixia Xu, and Yuqiu Zhao: Full asymptotic expansions of the Landau constants via a difference equation approach, Applied Mahtematics and Computation, 219 (2012), 988-995.
Yutian Li, Saiyu Liu, Shuaixia Xu, and Yuqiu Zhao: Asymptotics of Landau constants with optimal error bounds, Constructive Approximation, 40 (2014), 281-305.
Y. T. Li and R. Wong: Global asymptotics for Stieltjes-Wigert polynomials, Analysis and Applications, 11 (2013), article no.: 1350028, 12 pages.
L.-H. Cao and Y.-T. Li: Linear difference equations with a transition point at the origin, Analysis and Applications, 12 (2014), 75-106.
L.-W. Long, Y.-T. Li, S.-Y. Liu and Y.-Q. Zhao: Real solutions of the first Painlevé equation with large initial data, Studies in Applied Mathematics, 139 (2017), 505-532.
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Partial Differential Equations
6.?????? D.-C. Chang and Y. Li: SubRiemannian geodesics in Grushin plane, J. Geom. Anal., 22 (2012), 800–826.
7.?????? O. Calin, D.C. Chang, J. Hu, and Y. Li: On heat kernels of a class of degenerate elliptic operators, J. Nonlinear Convex Anal., 12 (2011), 309–340.
8.?????? D.-C. Chang and Y. Li: Small time asymptotics of the heat kernels for the Heisenberg subLaplacian and step two Grushin operator, Proceedings of the Royal Society A, 471 (2015), article no.: 20140943. 19 pages.
9.?????? Peter Greiner and Yutian Li: A fundamental solution for a nonelliptic partial differential operator, II, Analysis and Applications, to appear.
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Scientific Computing
10.?? Y. Li and J. Zhu: E?cient approximations of dispersion relations in optical waveguides with varying refractive-index pro?les, Optics Express, 23 (2015), 11952–11964.
11.?? J. Zhu and Y. Li: A new approach of eigenmodes for varying refractive-index pro?le’s waveguides, IEEE Trans. Microw. Theory Tech., 64, no. 10 (2016), 3131–3138.
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Mathematical Finance
12.?? J. Han, M. Gao, Q. Zhang, and Y. Li: Option prices under stochastic volatility, Applied Mathematics Letters, 26 (2013), 1–4.
13.?? X. Guo and Y. Li: Valuation of American options under the CGMY model, Quantitative Finance, 16 no. 10 (2016), 1529–1540.
14.?? H. Song, K. Zhang, and Y. Li, Finite element and discontinuous Galerkin methods with perfect matched layers for American options, Numer. Math. Theory Methods Appl.,10 (2017), 829-851.