Professor of Mathematics, Head of Mathematical Sciences Department
Phone: +64 9 921 9999 extn 8433
Email: email@example.comPhysical Address:
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 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.
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.
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
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.
Gaurav Kapoor (MSc), Working title of thesis: Leveraged ETFS options pricing under Heston dynamics, Auckland University of Technology.
Past Postgraduate Students
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 Recent Publications
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. G. Beer and J. Cao, Oscillation revisited, Set-Valued Var. Anal. 25 (2017), 603-616.
4. K. Li and J. Cao, Pairwise k-semi-stratifiability and topological ordered spaces, Topology Appl. 222 (2017), 139-151.
5. A. Bhowmik and J. Cao, Rational expectations equilibria: existence and representation, Econ. Theory Bull. 4 (2016), 367-386.
6. 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.
7. J. Cao and A.H. Tomita, Bornologies, topological games and function spaces, Topology Appl. 184 (2015), 16-28.
8. 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.
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 Appl. 169 (2014), 148-155.
11. A. Bhowmik and J. Cao, On the core and Walrasian expectations equilibrium in infinite dimensional commodity spaces, Econom. Theory 53 (2013), 537-560.
12. A. Bhowmik and J. Cao, Robust efficiency in mixed economies with asymmetric information, J. Math. Econom. 49 (2013), 49-57.
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 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