Professor of Mathematics, Head of Mathematical Sciences Department
Phone: +64 9 921 9999 extn 8433
Room WT117A, Level One, AUT Tower
2-14 Wakefield Street
BSc in Applied Mathematics, Tianjin University
MSc in Mathematics, Chinese Academy of Sciences
PhD in Mathematics, The University of Auckland
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
Prof Cao has taught undergraduate and postgraduate courses in Mathematics and Applied Mathematics at all levels.
Currently, he is involving with teaching two undergraduate courses MATH604 Financial Mathematics and MATH700 Financial Modelling and Computation, and two postgraduate courses: MATH802 Advanced Financial Modelling and Analytics and STAT804 Optimization and Operations Research.
Prof Cao's research interests are within several inter-related areas: Financial Mathematics, Mathematical Economics, Mathematical 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.
Rewat Khanthaporn (PhD), Working title of thesis: Analytic methods in finance with applications to portfolio and risk management, 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.
Zexi Huang (MSc), Working title of thesis: Aumann's core-Walras equivalence theorem in economies with differential information, Minnan Normal University.
Biyuan Wang (MSc), Working title of thesis: 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.
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. 20 (2018), 1359-1379.
2. A. Bhowmik and J. Cao, Ex-post core, fine core and rational expectations equilibrium allocations, 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
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 Adjunct Professor (福建省闽江学者), Minnan Normal University, China, 2014-2016
Finalist of the Vice Chancellor Award for Research Excellence, Auckland University of Technology, 2014
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 grant for Learning and Teaching Enabled by Technology (LATENT), Auckland University of Technology, 2012 (with Hyuck Chung, Alla Shymanska and Alna Van Der Merwe)
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)
New Zealand Science and Technology Post-doctoral Fellowship, The University of Auckland, 2002-2005
JSPS (Japan Society for the Promotion of Science) Post-doctoral Fellowship, Ehime University, 2000-2002
The Vice-Chancellor's Prize for the Best Doctoral Thesis in the Faculty of Science in 1998-1999, The University of Auckland, 2000