I am an Assistant Professor in the Department of Finance and Risk Engineering. My B.S. is from University of California at Santa Barbara (2003), my M.S. from University of Southern California (2007), and Ph.D. in Applied Mathematics from Brown University (2010).
My research focuses on filtering theory, parameter estimation, stochastic control, and financial mathematics. Specific problems I've studied include model design and calibration for pricing of volatility derivatives, statistical inference for hidden economic indicators, and optimal strategies for investment in markets with unobserved factors. My work provides detailed mathematical analysis while emphasizing a deeper understanding of finance and risk management. My interdisciplinary interests allow me to explore new research directions in financial mathematics, such volatility markets, markets with latent states, high-frequency trading, market microstructure, and financial data analysis.
My past appointments were as a postdoctoral fellow and lecturer at Princeton in the Department of Operations Research and Financial Engineering from 2010 to 2013, and as a lecturer at the University of Sydney in the School of Mathematics & Statistics from 2013 to 2015. In Spring 2015 I visited the Institute of Pure and Applied Mathematics at UCLA and participated in the workshop series on “Broad Perspectives and New Directions in Financial Mathematics.” An article related to the IPAM program is available here.
Currently, I am an associate editor for Risk and Decision Analysis. I co-organized the 2017 2nd Annual Eastern Conference on Mathematical Finance, and also the first conference on New Ideas & Cutting-Edge Developments in Fintech.
University of California at Santa Barbara, 2003
Bachelor of Science, Mathematical Sciences
University of Southern California, 2007
Master of Science, Financial Mathematics
Brown University, 2010
Doctor of Philosophy, Applied Mathematics
Filtering and Portfolio Optimization:
- Backward SDEs for Control with Partial Information, to appear in Mathematical Finance (2018) arXiv, journal
- Pairs Trading of Two Assets with Uncertainty in Co-Integration's Level of Mean Reversion, (with S. Lee), International Journal of Theoretical and Applied Finance, Vol. 19, No. 8, (2016) pp. (TBD). SSRN, journal
- Perturbation Analysis for Investment Portfolios Under Partial Information with Expert Opinions, (with J.P. Fouque and R. Sircar), SIAM Journal on Control and Optimization Vol. 55, No. 3, (2017) pp. 1534-1566 SSRN, journal
- Filtering and Portfolio Optimization with Stochastic Unobserved Drift In Asset Returns (with J.P. Fouque and R. Sircar), Communications in Mathematical Sciences, Vol. 13, No. 4, (2015) pp. 935-953 SSRN, journal
- Dimension Reduction in Discrete Time Portfolio Optimization with Partial Information, SIAM J. on Financial Mathematics, Vol. 4, No. 1, (2013) pp. 916-960. SSRN, journal
- Statistics of VIX Futures and Applications to Trading Exchange-Traded Products, (with M. Avellaneda) Journal of Investment Strategies, (2018) 7(2):1-33. (2017) SSRN, journal
- Analysis of VIX Markets with a Time-Spread Portfolio, Applied Mathematical Finance, Vol. 23, No. 5, (2016) pp. 374-408 SSRN, journal
- Extreme-Strike Comparisons and Structural Bounds for SPX and VIX Options, SIAM Journal on Financial Mathematics, Vol. 9, No. 2, pp. 401-434 (2018) SSRN, journal
- A Regime-Switching Heston Model for VIX and S&P500 Implied Volatilities (with R. Sircar), Quantitative Finance, Vol. 14, No. 10, (2014) pp. 1811-1827. SSRN, journal
- Implied Filtering Densities on the Hidden State of Stochastic Volatility, (with C. Fuertes) Applied Mathematical Finance, Vol. 21, No. 6, (2014) pp. 483-522. SSRN, journal, arXiv
Trading with Price Impact:
- Price Impact of Large Orders Using Hawkes Processes, (with L. R. Amaral) under review (2016) SSRN
- Singular Perturbation Expansion for Utility Maximization with Order-ε Linear Price Impact, (with S. Chandra) under review (2017) SSRN
Multiscale Filtering and Parameter Estimation:
- Dimension Reduction in Statistical Estimation of Partially-Observed Multiscale Processes (with K. Spiliopoulos) to appear in SIAM Journal on Uncertainty Quantification (2017) Vol. 5, No. 1, 1220–1247. arXiv, journal
- Filtering the Maximum Likelihood in Multiscale Problems (with K. Spiliopoulos), SIAM J. on Multiscale Modeling and Simulation, Vol. 12, No. 3, (2014) pp. 1193-1229 (37 pages). arXiv, journal
- Nonlinear Filtering for Hidden Markov Models with Fast Mean-Reverting States, SIAM J. on Multiscale Modeling and Simulation, Vol. 10, No. 3, (2012) pp. 906-935. arXiv, journal
- Filtering Fast Mean Reverting Processes, Asymptotic Analysis, Vol. 70, No. 3-4, (2010) pp. 155-176. SSRN, journal
- Book Review: Numerical Solutions of Stochastic Differential Equations with Jumps in Finance, by E. Platen and N. Bruti-Liberati, Quantitative Finance, Vol. 13, No. 9, (2013) pp. 1353-1355. journal
- Notes on Nonlinear Filtering: Theory and Applications Stochastic Analysis Seminar in the Department of Operations Research and Financial Engineering at Princeton University, (February 2011) arXiv
- Introduction to Stochastic Differential Equations (SDEs) for Finance (course notes for masters-degree students) arXiv