Professor Jiling Cao

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Professor of Mathematics, Head of Mathematical Sciences Department

Phone: +64 9 921 9999 extn 8433

Email: jiling.cao@aut.ac.nz

Physical Address:

Level One, AUT Tower
2-14 Wakefield Street
Auckland Central 



Postal Address:
Department of Mathematical Sciences
School of Engineering, Computer and Mathematical Sciences
Auckland University of Technology
Private Bag 92006, Auckland 1142
New Zealand 

Qualifications:

BSc in Applied Mathematics, Tianjin University

MSc in Mathematics, Chinese Academy of Sciences

PhD in Mathematics, The University of Auckland

 

Memberships and Affiliations:

Member of the American Mathematical Society

Fellow of the New Zealand Mathematical Society

Reviewer of Mathematical Reviews, the American Mathematical Society

Reviewer of Zentralblatt MATH, the European Mathematical Society and the Heidelberg Academy of Science

Editor of Questions and Answers in General Topology, Japan Publications Trading Co Ltd. 

Editor of International Journal of Mathematics and Statistics, Ceser Publications 

Biography:

Jiling Cao (Chinese: 曹继岭) taught himself mathematics under the light of an oil lamp in a poor village near Nanyang (a prefectural-level city) in China. He was inspired to study mathematics when he was about 11 or 12 to take after the national hero at that time -Jingrun Chen (Chinese: 陈景润), a top mathematician. He borrowed his teacher's reference books and began studying each night. Mathematics quickly became his life. He completed his undergraduate studies in China and then moved to Auckland to complete his doctorate.
 
Prof Cao was the recipient of the inaugural Vice Chancellor's Prize for the Best Doctoral Thesis in the Faculty of Science in 1998-1999, The University of Auckland. In 2000, he was awarded a post-doctoral research fellowship by the Japan Society for the Promotion of Science (JSPS) at Ehime University. In 2002, he was awarded a New Zealand Science and Technology (NZST) post-doctoral fellowship.

He moved to AUT as a research lecturer in 2006, when the undergraduate mathematical sciences programme just started. In 2013, he was promoted to a full professor. Since January 2015, he has been the Head of Mathematical Sciences Department. Prof Cao has published intensively in mathematical analysis, general/set-theoretic topology, mathematical game theory, mathematical modelling in economics and finance. He was an investigator of a Marsden Fund research project from 2005 and 2007. Currently, he is an investigator of a research project funded by the National Natural Science Foundation of China. He writes reviews for Mathematical Reviews and Zentralblatt MATH, and has refereed research articles for over 40 international journals. Prof Cao also held visiting professorships in Brazil, China and India, and has delivered invited addresses at many institutes and international conferences.

Prof Cao stresses to his students that most of the things that make life easy is because of mathematics, and there will be no technological advancements if people stop training in the field. In his view, the problem solving skills that come with learning mathematics makes it a highly sought after industry.

Teaching Areas:

Prof Cao has taught undergraduate and postgraduate courses in mathematics and applied mathematics at all levels.

Currently, he is involving with teaching the undergraduate course MATH604 Mathematics of Finance, and three postgraduate courses: MATH802 Financial Mathematics, MATH804 Financial Models and Decision Analysis, and STAT804 Optimization and Operations Research.

Research Areas:

Prof Cao's research interests are within several inter-related areas: Financial mathematics, Mathematical economicsMathematical analysis and Analytic topology. Until now, he has authored and co-authored over 80 research outputs in these areas.

In 2016, Prof Cao founded the Financial Mathematics and Computation Research Group (AUT-FMC) in the Department of Mathematical Sciences at AUT. This research group aims to bring together complementary expertise in financial mathematics, financial economics and data statistics to undertake multi-disciplinary research projects. More details about the current members, research projects and activities of AUT-FMC can be found from the website: https://sites.google.com/site/autfmc/

Current Postgraduate Students   

Beidi Peng (PhD), Working title of thesis: A study on optimal portfolio selections, Auckland University of Technology.  

Shu Su (PhD), Working title of thesis: Stochastic volatility models under time-changed Levy processes and applications to VIX derivatives, Auckland University of Technology. 

Reza Mossavi Mohseni (PhD), Working title of thesis: Mathematical analysis of the chaotic behaviour in monetary policy games, Auckland University of Technology.

Biyuan Wang (MSc), Working title of dissertation: Option pricing under the Heston-CIR model with stochastic interest rate and transaction costs, Auckland University of Technology.  

Past Postgraduate Students 

Gaurav Kapoor (MSc), Title of thesis: Pricing Leveraged ETFS options under Heston dynamics, Auckland University of Technology, 2018.  

Biyuan Wang (BSc Honours), Title of dissertation: A robust study and numerical solution of the Black-Scholes option pricing model, Auckland University of Technology, 2017.  

Su Yuan Chan (MSc), Title of thesis: Assessing core stable coalitions based on social network structures, Auckland University of Technology, 2017 

The Raihana Nazirah Roslan (PhD), Title of thesis: Pricing variance swaps under stochastic volatility and stochastic interest rate, Auckland University of Technology, 2016. 

Gaurav Kapoor (BSc Honours), Title of dissertation: Comparison of risk measures in finance, Auckland University of Technology, 2016.     

Tianying Wu (MSc), Title of thesis: Supermodular games with differential information for finitely many players, Auckland University of Technology, 2015.        

Bing (Frank)  Huang (PhD), Title of thesis: Real option games with stochastic volatility, Auckland University of Technology, 2015.

Anuj Bhowmik (PhD), Title of thesis: Blocking efficiency and competitive equilibria in economies with asymmetric information, Auckland University of Technology, 2013.

Felipe Eduardo Lillo Viedma (PhD), Title of thesis: Coloured-edge graph approach for modelling of multimodal networks, Auckland University of Technology, 2011.

Leon Luo (BMathSc Honours), Title of dissertation: On the Attouch-Wets topology and convex optimization, Auckland University of Technology, 2011.

Rocko Chen (BMathSc Honours), Title of dissertation: Incomplete financial market: Theory and practice, Auckland University of Technology, 2010.

Bing (Frank) Huang (BMathSc Honours), Title of dissertation: Game theory and applications to duopoly and oligopoly models, Auckland University of Technology, 2010.

Junhui Kim (PhD), Title of thesis: On star covering properties, Ehime University, 2002. 

Publications:

Selected Publications in Financial Mathematics and Mathematical Economics

1. J. Cao, T.R. Nazirah Roslan and W. Zhang, Pricing variance swaps in a hybrid model of stochastic volatility and interest rate with regime-switching, Methodol. Comput. Appl. Probab., to appear. 

2. A. Bhowmik and J. Cao, Ex-post core, fine core and rational expectations equilibrium allications, J. Math. Econom. 74 (2018), 128-138. 

3. A. Bhowmik and J. Cao, Rational expectations equilibria: existence and representation, Econ. Theory Bull. 4 (2016), 367-386. 

4. J. Cao, G. Lian and T.R. Nazirah Roslan, Pricing variance swaps under stochastic volatility and stochastic interests, Appl. Math. Comput. 277 (2016), 72-81.  

5. A. Bhowmik, J. Cao and N.C. Yannelis, Aggregate preferred correspondence and the existence of a maximin REE, J. Math. Anal. Appl. 414 (2014), 155-156. 

6. B. Huang, J. Cao and H. Chung, Strategic real options with stochastic volatility in a duopoly, Chaos Solitons Fractals, 58 (2014), 40-51. 

7. A. Bhowmik and J. Cao, On the core and Walrasian expectations equilibrium in infinite dimensional commodity spaces, Econom. Theory 53 (2013), 537-560.

8. A. Bhowmik and J. Cao, Robust efficiency in mixed economies with asymmetric information, J. Math. Econom. 49 (2013), 49-57. 

Selected Publications in Analytic Topology and Mathematical Analysis 

9. G. Beer and J. Cao, Oscillation revisited, Set-Valued Var. Anal. 25 (2017), 603-616. 

10. K. Li and J. Cao, Pairwise k-semi-stratifiability and topological ordered spaces, Topology Appl. 222 (2017), 139-151. 

11. F. Lin, C. Liu and J. Cao, Two weak forms of countability axioms in free topological groups, Topology Appl. 207 (2016), 96-108.

12. J. Cao and A.H. Tomita, Bornologies, topological games and function spaces, Topology Appl. 184 (2015), 16-28.

13. J. Cao and H.J.K. Junnila, Hereditarily normal Wijsman hyperspaces are metrizable, Topology Appl. 169 (2014), 148-155. 

14. J. Cao, H.J.K. Junnila and W.B. Moors, Wijsman hyperspaces: Subspaces and embeddings, Topology Appl. 159 (2012), 1620-1624. 

15. J. Cao, The Baire property in hit-and-miss hypertopologies, Topology Appl. 157 (2010), 1325-1334. 

16. J. Cao and H.J.K. Junnila, Amsterdam properties of Wijsman hyperspaces, Proc. Amer. Math. Soc. 138 (2010), 769-776. 
 

Full List of Publications

For a relatively comprehensive list of Prof Cao's publications, please use either MathSciNet https://mathscinet-ams-org.ezproxy.aut.ac.nz/mathscinet/search.html to search items under the name "Cao, Jiling" (Author ID: 318403), or visit Google Scholar https://scholar.google.co.nz/citations?user=cPWRHOgAAAAJ&hl=en&oi=sra or Research Gate https://www.researchgate.net/profile/Jiling_Cao 

Awards:

A National Natural Science Foundation of  China grant for the research project Characterizations of generalized metric properties in free (para) topological groups, 2016-2019 (with Fucai Lin et al.)

Min Jiang Scholar and Visiting Professor, Minnan Normal University, China, 2014-2016 

Dean's Award for Research Excellence, Faculty of Design and Creative Technologies, Auckland University of Technology, 2013 

FAPESP Visiting Professor, University of Sao Paulo, Brazil, 2008, 2013 

Fellow of the New Zealand Mathematical Society (FNZMS), 2012 

A travel grant to visit the University of Helsinki by Maguns Ehrnrooth Foundation, Finnish Society of Sciences and Letters, 2008 

Rani and Asutosh Ganguli Visiting Professor, University of Kolkata, India, 2008 

A Marsden Fund grant for the research project Analytic topology and its applications, 2005-2007 (with Warren B. Moors

The Vice-Chancellor's Prize for the Best Doctoral Thesis in the Faculty of Science in 1998-1999, The University of Auckland, 2000