## ResearchI work on various problems related to probability, mathematical finance and applications. Currently I am interested in robust portfolio theory, optimal transport as well as information geometry. You are welcome to visit my arXiv and Google Scholar profiles.Working papers- Statistical Manifolds from Optimal Transport. (2017) Link. - On Time-Consistent Conditional Expectation Under Probability Distortion. With Jin Ma and Jianfeng Zhang. Manuscript in preparation. Submited papers and preprints- On Portfolios Generated by Optimal Transport. (2017) Link - Cover's Universal Portfolio, Stochastic Portfolio Theory and the Numeraire Portfolio With Christa Cuchiero and Walter Schachermayer). Under revision at Mathematical Finance. Link. - Universal Portfolios in Stochastic Portfolio Theory. (2015) Link. Accepted and published papers- Random Walks and Induced Dirichlet Forms on Self-similar Sets with Ka-Sing Lau and Shi-Lei Kong. Advances in Mathematics (2017). Link. - Exponentially Concave Functions and a New Information Geometry with Soumik Pal. To appear in Annals of Probability. Link. - Volatility Harvesting in Theory and Practice With Paul Bouchey and Vassilii Nemtchinov. The Journal of Wealth Management (2015). Link. - The Geometry of Relative Arbitrage With Soumik Pal. Mathematics and Financial Economics (2016). Link. - Optimization of Relative Arbitrage Annals of Finance (2015). Link. Other manuscripts- Geometry and Optimization of Relative Arbitrage PhD Thesis (2016). University of Washington. Link. - Energy, Entropy, and Arbitrage With Soumik Pal. Unpublished manuscript (2013). Link. - Boundary Theory of Random Walk and Fractal Analysis Mphil Thesis (2011). The Chinese University of Hong Kong. Link. - Induced Measures of Simple Random Walks on Sierpinski Graphs Unpublished manuscript (2011). Link. ## Invited talks(2018, Apr) Probability Seminar, University of Colorado, Boulder.(2017, Dec) Analysis Seminar, University of Pittsburgh, Pennsylvania. (2017, Dec) Probability Seminar, University of Washington, Seattle. (2017, Oct) Mathematical Finance and Probability Seminar, Rutgers University, New Jersey. (2017, Oct) Mathematical Finance Colloquium, University of Southern California, Los Angeles. (2017, Aug) Department of Mathematics seminar, The Chinese University of Hong Kong, Hong Kong. (2017, May) Vienna Seminar in Mathematical Finance and Probability, University of Vienna, Vienna. (2017, Apr) CFMAR seminar, University of California, Santa Barbara. (2017, Mar) 8th Western Conference on Mathematical Finance, Seattle. (2016, Nov) SIAM Conference on Financial Mathematics & Engineering, Austin. (2016, Sep) Probability and Statistics Seminar, University of Southern California. (2016, Mar) CFRM Seminar, University of Washington. (2016, Jan) AMS Special Session, Joint Mathematics Meeting 2016. (2015, Nov) Math Finance Colloquium, University of Southern California. (2015, Oct) Financial/Actuarial Mathematics seminar, University of Michigan. (2015, Sep) Probability and Computational Finance Seminar, Carnegie Mellon University. (2015, May) Stochastic Portfolio Theory and Related Topics, Columbia University. (2015, Apr) CFMAR seminar, University of California, Santa Barbara. (2014, Dec) Statistics seminar, The Chinese University of Hong Kong. (2014, July) UseR! 2014, University of California, Los Angeles. (2014, Mar) Statistics seminar, The Chinese University of Hong Kong. (2013, Apr) Probability seminar, University of Washington. ## TeachingIn Fall 2017 I am teaching a PhD topics course on Portfolio Theory, Optimal Transport and Information Geometry. See Blackboard for more information.Future courses: Spring 2018: MATH 512 Computational Finance and MATH 530b Mathematical Finance Previous courses at USC:Spring 2017: MATH 512 Computational Finance (Financial Informatics and Simulation), MATH118 Introduction to Statistics Fall 2016: MATH 125 Calculus I Previous courses at UW:Spring 2016: MATH 309 Linear Analysis Winter 2015: MATH 307 Ordinary differential equations Autumn 2014: MATH 308 Matrix Algebra ## ComputingR ProgrammingFor beginners I recommend The Art of R Programming by Norman Matloff. A good (intermediate-advanced) reference is Advanced R by Hadley Wickham. R Packages- RelValAnalysis. (Relative Value Analysis) Available on CRAN. Current version: 1.0 (June 26, 2014). This R package implements results in stochastic portfolio theory and the energy-entropy framework in Pal and Wong (2013). Click here for introductory slides presented in the useR! 2014 Conference. The R codes presented in the slides are collected here. |