Professor Jiling Cao

Jiling Cao

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 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 (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: Mathematical analysis, Mathematical game theory, Mathematical modelling in economics and finance, General and Set-theoretic topology. Until now, he has authored and co-authored over 80 research outputs in these areas.

 

Current Postgraduate Students   

Shu Su (PhD), Working title of thesis: Mathematical modelling on pricing the second generation volatility derivatives, Auckland University of Technology. 

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

Gaurav Kapoor (MSc), Working title of thesis: Performance and investment potential of VIX derivatives, Auckland University of Technology.

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

 

Past Postgraduate Students  

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 Recent Publications 

1. G. Beer and J. Cao, Oscillation revisited, Set-Valued and Variational Analysis 25 (2017), 603-616. 

2. J. Cao, Three open problems on the Wijsman topology, Questions and Answers in General Topology 35 (2017), 49-58.

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

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

5. J. Cao, G. Lian and T.R. Nazirah Roslan, Pricing variance swaps under stochastic volatility and stochastic interests, Applied Mathematics and Computation 277 (2016), 72-81. 

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

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

8. A. Bhowmik, J. Cao and N.C. Yannelis, Aggregate preferred correspondence and the existence of a maximin REE, Journal of Mathematical Analysis and Applications 414 (2014), 155-156. 

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

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

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

12. A. Bhowmik and J. Cao, Robust efficiency in mixed economies with asymmetric information, Journal of Mathematical Economics 49 (2013), 49-57.

13. H. Zhao, X. Rong and J. Cao, Optimal investment with multiple risky assets for an insurer in an incomplete market, Discrete Dynamics in Nature and Society 2013, Article ID 751846, 12 pages.

14. A. Bhowmik and J. Cao, Blocking efficiency in an economy with asymmetric information, Journal of Mathematical Economics 48 (2012), 396-403.

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

 

Full List of Publications

For a relatively comprehensive list of Prof Cao's publications, please use either the MathSciNet website to search under MR Author ID 318403, or the Google Scholar website, or the Research Gate website to search under the name 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


Last updated: 22-Sep-2017 10.28am

The information on this page was correct at time of publication. For a comprehensive overview of AUT qualifications, please refer to the Academic Calendar.