National Science Foundation Grant in Applied Mathematics, DMS-1613170, 2016-2019.
National Science Foundation CAREER Grant in Applied Mathematics, DMS-0955463, 2010-2016 (PI).
National Science Foundation, Division of Mathematical Sciences, Computational Foundations for Emerging Science Frontiers, DMS-1118673, 2011-2015 (PI, joint with Lifeng Lai and H. Vincent Poor).
National Science Foundation Applied Mathematics Research Grant, DMS-0906257, 2009-2013 (PI).
National Science Foundation, DMS-1108593, Workshop on Stochastic Analysis in Finance and Insurance, May 2011 (PI, joint with Mihai Sirbu and Gordan Zitkovic).
National Science Foundation Coffes/Applied Mathematics Research Grant, DMS-0604491, 2006-2009 (PI).
Horace H. Rackham Faculty Grant and Fellowship, University of Michigan, Ann Arbor, MI, 2005-2006.
Independent Contractor for the U.S. Army Pantheon Project (2005-2006).
CKER Research Grant, Society of Actuaries (joint with Mike Ludkovski) (2007-2008).
AERF Research Grant, The Actuarial Foundation (joint with Jenny Young) (2009-2010).
CKER Research Grant, Society of Actuaries (joint with Jenny Young) (2012-2013).
Martingale optimal transport with stopping , (with Alex Cox and Yavor Stoev), to appear in SIAM Journal on Control and Optimization [SSRN], [ArXiv].
On the controller-stopper problems with controlled jumps , (with Jiaqi Li), to appear in Applied Mathematics and Optimization [ArXiv], [Article].
Solvability of the non-linear Dirichlet problem with Integro-Differential operators , (with Qingshuo Song), to appear in SIAM Journal on Control and Optimization , [ArXiv].
Quantile Hedging in a Semi-Static Market with Model Uncertainty, (with Gu Wang), to appear in Mathematical Methods of Operations Research. [SSRN], [ArXiv], [Article].
Rate Control under Heavy Traffic with Strategic Servers , (with Amarjit Budhiraja and Asaf Cohen), to appear in Annals of Applied Probability, [ArXiv].
Efficient Byzantine Sequential Change Detection, (with Georgios Fellouris and Lifeng Lai), to appear in the IEEE Transactions on Information Theory , [ArXiv], [Article].
Distribution-Constrained Optimal Stopping, (with Christopher W. Miller), to appear in Mathematical Finance [SSRN], [ArXiv].
On Zero-sum Optimal Stopping Games, (with Zhou Zhou), to appear in Applied Mathematics and Optimization. [SSRN], [ArXiv], [Article].
On the Market Viability under Proportional Transaction Costs , (with Xiang Yu), to appear in Mathematical Finance. [SSRN], [ArXiv], [Article].
Randomized dynamic programming principle and Feynman-Kac representation for optimal control of McKean-Vlasov dynamics , (with Andrea Cosso and Huyen Pham), to appear in Transactions of the American Mathematical Society . [HAL], [ArXiv], [Article].
Risk Sensitive Control of the Lifetime Ruin Problem , (with Asaf Cohen), to appear in Applied Mathematics and Optimization, [SSRN], [ArXiv], [Article].
Published Journal Articles
On Arbitrage and Duality under Model Uncertainty and Portfolio Constraints , (with Zhou Zhou), Mathematical Finance , Vol 27, No. 4, 988-1012, 2017. [SSRN], [ArXiv], [Article].
Super-hedging American Options with Semi-static Trading Strategies under Model Uncertainty, (with Zhou Zhou), International Journal of Theoretical and Applied Finance , 20 (6), 10 pages. [SSRN], [ArXiv], [Article].
On the Robust Dynkin Game, (with Song Yao), Annals of Applied Probability, 2017, 27 (3), 1702-1755. [SSRN], [ArXiv], [Article]
High-Roller Impact: A Large Generalized Game Model of Parimutuel Wagering, (with Alex Munk), Market Microstructure and Liquidity, 2017, 3 (1), 45 pages. [SSRN], [ArXiv], [Article],
[News Article]
Ergodicity of robust switching control and nonlinear system of quasi variational inequalities , (with Andrea Cosso and Huyen Pham), SIAM Journal on Control and Optimization , 2017, 55(3), 1915–1953. [HAL], [ArXiv], [Article]
Optimal Stopping with Random Maturity under Nonlinear Expectations, (with Song Yao), Stochastic Processes and Their Applications , 2017, 127(8), Pages 2586-2629 [ArXiv], [Article].
Arbitrage, hedging and utility maximization using semi-static trading strategies with American options, (with Zhou Zhou), Annals of Applied Probability, 2016, 26 (6), 3531-3558. [SSRN], [ArXiv], [Article]
A rank based mean field game in the strong formulation , (with Yuchong Zhang), Electronic Communications in Probability , 2016, Vol. 21, paper no. 72, 1-12. [SSRN], [ArXiv], [Article]
Robust feedback switching control: dynamic programming and viscosity solutions , (with Andrea Cosso and Huyen Pham), SIAM Journal on Control and Optimization, 54(5), 2594–2628, October 2016. [ArXiv], [HAL], [Article].
Stochastic Perron for Stochastic Target Problems, (with Jiaqi Li), Journal of Optimization Theory and Applications, Volume 170, September 2016, Issue 3, 1026–1054.[ArXiv], [Article].
Fundamental Theorem of Asset Pricing under Transaction costs and Model uncertainty, (with Yuchong Zhang), Mathematics of Operations Research , 41 (3), 2016, 1039 - 1054. [SSRN], [ArXiv], [Article].
Optimally Investing to Reach a Bequest Goal , (with Jenny Young), Insurance: Mathematics and Economics, Volume 70, September 2016, 1–10. [SSRN], [ArXiv], [Article].
Minimizing the Probability of Lifetime Drawdown under Constant Consumption , (with Bahman Angoshtari and Jenny Young), Insurance: Mathematics and Economics, Volume 69, July 2016, 210–223. [SSRN], [ArXiv], [Article].
Optimal Investment to Minimize the Probability of Drawdown, (with Bahman Angoshtari and Jenny Young), Stochastics, Volume 88 (6), 2016, 946-958. [SSRN], [ArXiv], [Article]
On an Optimal Stopping Problem of an Insider , (with Zhou Zhou), Teoriya Veroyatnoste i i ee Primeneniya, 61 (1), 181-186, 2016; also published as Theory of Probability and its applications 61-1 (2017), pp. 133-139 (SIAM version) [SSRN], [ArXiv], [Russian version], [SIAM version].
On a Stopping Game in continuous time , (with Zhou Zhou),Proceedings of the AMS 144 (8), 3589-3596, 2016. [ArXiv], [Article].
An alpha-Stable Limit Theorem Under Sublinear Expectation , (with Alex Munk), Bernoulli, 22 (4), 2548-2578, 2016. [ArXiv].
Stochastic Perron for Stochastic Target Games, (with Jiaqi Li), Annals of Applied Probability, 26 (2), 1082-1110, 2016. [ArXiv/Article].
Purchasing Term Life Insurance to Reach a Bequest while Consuming, (with David Promislow and Jenny Young), SIAM Journal on Financial Mathematics, 7(1), 183–214, 2016. [SSRN], [ArXiv], [Article].
Minimizing the Expected Lifetime Spent in Drawdown under Proportional Consumption , (with Bahman Angoshtari and Jenny Young), Finance Research Letters, Volume 15, Pages 106–114, 2015. [SSRN], [ArXiv], [Article].
Doubly Reflected BSDEs with Integrable Parameters and Related Dynkin Games , (with Song Yao),Stochastic Processes and Their Applications , 125 (12) 4489–4542, 2015. [ArXiv], [Article].
Weak reflection principle for Levy processes , (with Sergey Nadtochiy), Annals of Applied Probability, 25 (6), 3251-3294, 2015. [SSRN], [ArXiv], [Article].
Purchasing Term Life Insurance to Reach a Bequest Goal: Time-Dependent Case , (with David Promislow and Jenny Young), North American Actuarial Journal , 19 (3), 224-236, 2015. [ArXiv], [Article].
Comparing the $G$-Normal Distribution to its Classical Counterpart, (with Alexander Munk), Communications on Stochastic Analysis , 9 (1), 1-18, 2015. [ArXiv], [SSRN], [Article].
On hedging American options under model uncertainty , (with Yu-Jui Huang and Zhou Zhou), SIAM Journal on Financial Mathematics (SIFIN), , 6(1), 425–447, 2015.[SSRN], [ArXiv], [Article].
Byzantine Fault Tolerant Distributed Quickest Change Detection, (with Lifeng Lai), SIAM Journal on Control and Optimization , 53(2), 575-591, 2015. [ArXiv], [Article].
Quickest Detection with Discretely Controlled Observations, (with Ross Kravitz), Sequential Analysis, 34 (1), 77-133, 2015. [ArXiv], [Article].
Stochastic Perron's Method for the Probability of lifetime ruin problem under transaction costs, (with Yuchong Zhang), SICON (SIAM Journal on Control and Optimization), 53(1), 91-113, 2015. [SSRN],[ArXiv], [Article].
Minimizing the Probability of Lifetime Ruin Under Ambiguity Aversion , (with Yuchong Zhang), SICON (SIAM Journal on Control and Optimization), 53(1), 58-90, 2015. [SSRN],
[ArXiv], [Article].
A note on the Fundamental Theorem of Asset Pricing under model uncertainty , (with Yuchong Zhang and Zhou Zhou), Risks , 2(4), 425-433, 2014. [SSRN], [ArXiv], [Article].
On the Robust Optimal Stopping Problem , (with Song Yao), SIAM Journal on Control and Optimization, 52(5), 3135-3175, 2014. [SSRN], [ArXiv], [Article].
Liquidation in Limit Order Books with Controlled Intensity, (with Mike Ludkovski), Mathematical Finance, Volume 24, Issue 4, pages 627-650, October 2014. [SSRN
], [ArXiv
], [Article
]
Bayesian Quickest Change Point Detection with Sampling Right Constraints, (with Jun Geng and Lifeng Lai), IEEE Transactions on Information Theory, Volume 60, No. 10, 6474-6490, 2014. [Article].
Purchasing Life Insurance to Reach a Bequest Goal, (with David Promislow and Jenny Young), Insurance: Mathematics and Economics, Volume 58, 204-216, 2014. [ArXiv], [SSRN], [Article].
Quickest Search over Brownian Channels, (with Ross Kravitz), Stochastics, Volume 86, Issue 3, 473-490, 2014. [ArXiv], [Article].
A Stochastic Approximation for Fully Nonlinear Free Boundary Problems, (with Arash Fahim), Numerical Methods for Partial Differential Equations , Volume 30, Issue 3, pages 902-929, May 2014. [ArXiv], [Article].
A Note on Applications of Stochastic Ordering to Control Problems in Insurance and Finance, (with Nicole Bauerle), Stochastics, Volume 86, Issue 2, pages 330-340, 2014. [ArXiv], [Article].
Stochastic Perron's method and verification without smoothness using viscosity comparison: obstacle problems and Dynkin games, (with Mihai Sirbu), Proceedings of the American Mathematical Society , 142 (4), 1399-1412, 2014. [ArXiv], [Article].
On controller-stopper problems with jumps and their applications to indifference pricing of American options, (with Zhou Zhou), SIFIN (SIAM Journal on Financial Mathematics), 5 (1), 20-49, 2014. [ArXiv], [SSRN], [Article].
Optimal reinsurance and investment with unobservable claim size and intensity , (with Zhibin Liang), IME (Insurance: Mathematics and Economics), 55 (March 2014), Pages 156–166. [Article].
Optimal dividends in the dual model under transaction costs, (with Andreas Kyprianou and Kazutoshi Yamazaki), Insurance: Mathematics and Economics., 54, 133-143, 2014. [ArXiv], [SSRN], [Article]
On the Existence of Consistent Price Systems, (with Mikko S. Pakkanen and Hasanjan Sayit), Stochastic Analysis and Applications, 32, 152-162, 2014. [ ArXiv], [ Article]
Stochastic Perron's method for Hamilton-Jacobi-Bellman equations, (with Mihai Sirbu), SIAM Journal on Control and Optimization , 51(6), 4274-4294, 2013.[ArXiv], [SSRN], [Article].
Robust maximization of asymptotic growth under covariance uncertainty , (with Yu-Jui Huang) Annals of Applied Probability , 23 (5), 1817-1840, 2013. [ArXiv, Article
], [SSRN].
On optimal dividends in the dual model, (with Andreas Kyprianou and Kazutoshi Yamazaki), ASTIN Bulletin, 43 (3), 359-372. [ArXiv], [SSRN], [Article].
On the Impulse Control of Jump Diffusions, (with Tom Emmerling and Jose-Luis Menaldi), SIAM Journal on Control and Optimization , 51(3), 2612--2637, 2013. [PDF], [SSRN], [Article].
Life Insurance Purchasing to Maximize Utility of Household Consumption , (with Virginia R. Young), NAAJ, 17 (2), 1--22, 2013. [ArXiv], [Article].
A Weak Dynamic Programming Principle for Zero-Sum Stochastic Differential Games with Unbounded Controls, (with Song Yao), SIAM Journal on Control and Optimization , 51(3), 2036--2080, 2013. [ArXiv], [SSRN], [Article]
On the Multi-dimensional controller and stopper games, (with Yu-Jui Huang), SIAM Journal on Control and Optimization, 51 (2), 1263--1297, 2013. [ArXiv],[SSRN], [Article].
Stability of exponential utility maximization with respect to market perturbations, (with Ross Kravitz) Stochastic Processes and Their Applications, 123 (5), 1671-1690, 2013. [ArXiv
], [Article].
Outperforming the Market Portfolio with a Given Probability, (with Yu-Jui Huang and Qingshuo Song), Annals of Applied Probability , 22 (4) 1465--1494, 2012. [ArXiv, Article], [SSRN].
Stochastic Perron's method and verification without smoothness using viscosity comparison: the linear case, (with Mihai Sirbu), Proceedings of the American Mathematical Society , 140, 3645-3654, 2012. [ArXiv
], [Article]
Regularity of the Optimal Stopping Problem for Jump Diffusions, (with Hao Xing), SIAM Journal on Control and Optimization, 50 (3), 1337-1357, 2012.[ ArXiv], [Article].
Valuation equations for stochastic volatility models, (with Kostas Kardaras and Hao Xing), SIAM Journal on Financial Mathematics, 2012, 3, 351-373. [SSRN],
[ArXiv], [Article].
Strict Local Martingale Deflators and Pricing American Call-Type Options, (with Constantinos Kardaras and Hao Xing), Finance and Stochastics , (2012), 16(2), 275-291. [SSRN], [Arxiv], [Article].
Quadratic Reflected BSDEs with Unbounded Obstacles, (with Song Yao), Stochastic Processes and Their Applications, (2012), 122, 1155-1203. [ArXiv], [SSRN], [Article].
Proving the Regularity of the Minimal Probability of Ruin via a Game of Stopping and Control, (with Virginia R. Young), Finance and Stochastics (2011), 15 (4), 785-818. [SSRN], [ArXiv], [Article].
Optimal Trade Execution in Illiquid Markets, (with Mike Ludkovski), Mathematical Finance (2011), 21(4), 681-701. [ArXiv], [SSRN], [Article].
A Unified Framework for Pricing Credit and Equity Derivatives (with Bo Yang), Mathematical Finance, (2011), 21 (3), 493-517. [ PDF], [ArXiv], [SSRN], [Article].
On the Perpetual American Put Options for Level Dependent Volatility Models with Jumps, Quantitative Finance, (2011), 11 (3), 335-341. [ ArXiv], [ SSRN], [ Article].
Minimizing the Probability of Lifetime Ruin under Stochastic Volatility, (with Xueying Hu and Virginia R. Young), Insurance Mathematics and Economics (2011), 49 (2), 194-206. [ArXiv], [Article]
Optimal Stopping for Nonlinear Expectations, Part I (with Song Yao), Stochastic Processes and Their Applications (2011), 121 (2), 185-211. [SSRN], [Article].
Optimal Stopping for Nonlinear Expectations, Part II (with Song Yao), Stochastic Processes and Their Applications (2011), 121 (2), 212-264.
An older version where Part I and II appear together [ArXiv], [SSRN], [Article].
Pricing Asian Options for Jump Diffusions
(with Hao Xing), Mathematical Finance (2011), 21 (1), 117-143. [ArXiv], [SSRN], [Article].
On the Continuity of Stochastic Exit Time Control Problems, (with Qingshuo Song and Jie Yang), Stochastic Analysis and Applications (2011), 29, 1-13. [ArXiv], [Article].
Optimal Stopping for Dynamic Convex Risk Measures, (with Ioannis Karatzas and Song Yao), Illinois Journal of Mathematics, 54 (3), 1025-1067 (Fall 2010), A special volume in honor of Donald Burkholder. [ArXiv], [SSRN], [Article].
On the Stickiness Property, (with Hasanjan Sayit), Quantitative Finance, (2010), 10 (10), 1109-1112. [ArXiv], Article].
On the uniqueness of classical solutions of Cauchy problems, (with Hao Xing), Proceedings of the American Mathematical Society, (2010), 138 (6), 2061-2064. [ArXiv], [Article].
On the One-Dimensional Optimal Switching Problem , (with Masahiko Egami), Mathematics of Operations Research, 2010, 35 (1), 140-159. [ArXiv], [Article].
Inventory Management with Partially Observed Non-stationary Demand
(with Mike Ludkovski), Annals of Operations Research, 2010, 176 (1), 7-39. [ArXiv], [Article].
Optimal investment strategy to minimize occupation time (with Jenny Young), Annals
of Operations Research, 2010, 176 (1), 389-408. [ArXiv], [Article].
A Unified Treatment of Dividend Payment Problems under Fixed Cost and Implementation Delays,
(with Masa Egami), Mathematical Methods of Operations Research, 2010, 71 (2), 325-351. [ArXiv], [Article].
No Arbitrage Conditions For Simple Trading Strategies, (with Hasanjan Sayit), Annals of Finance, (2010), 6 (1), 147-156. [ArXiv], [Article].
Pricing American Options for Jump Diffusions by Iterating optimal stopping problems for Diffusions, (with Hao Xing), Mathematical Methods of Operations Research, (2009), 70 (3), 505-525. [ArXiv], [Article].
Analysis of the Optimal Exercise Boundary of American Options for Jump Diffusions (with Hao Xing), SIAM Journal on Mathematical Analysis (2009), 41 (2), 825-860. [ArXiv], [Article].
A Proof of the Smoothness of the Finite Time Horizon American Put Option for Jump Diffusions, SIAM Journal on Control and Optimization (2009), 48 (2), 551-572.
[ArXiv], [SSRN], [Article].
A Sequential Tracking of a Hidden Markov Chain Using Point Process Observations (with Mike Ludkovski), Stochastic Processes and Their Applications, 2009, 119 (6) 1792-1822.
[ArXiv ], [Article].
Valuation of Mortality Risk via the Instantaneous Sharpe Ratio: Applications to Life Annuities (with Moshe Milevsky, David Promislow, Virginia Young), Journal of Economic Dynamics and Control, (2009), 33 (3), 676-691.
[ArXiv ], [SSRN], [Article].
Online Change Detection for a Poisson Process with a Phase-Type Change-Time Prior Distribution (with Semih Sezer), Sequential Analysis, 2009, 28 (2), 218-250. [ArXiv] (an older version with a different title), [ArXiv]
Optimal Deferred Life Annuities to Minimize the Probability of Lifetime Ruin (with Jenny Young), North American Actuarial Journal (NAAJ), (2009) 13 (1), 141-154. [Article].
Relative Hedging of Systematic Mortality Risk (with Mike Ludkovski), NAAJ, (2009), 13 (1), 106-140. [Article].
Minimizing the Lifetime Shortfall or Shortfall at Death (with Jenny Young), Insurance: Mathematics and Economics, 2009, 44 (3), 447-458. [ArXiv], [Article].
Maximizing Utility of Consumption Subject to a Constraint on the Probability of Lifetime Ruin (with Virginia R. Young), Finance and Research Letters, (2008), 5 (4), 204-212.
[ArXiv], [Article].
Minimizing the Probability of Lifetime Ruin under Random Consumption (with Kristen Moore and Virginia R. Young), NAAJ, 2008, 12 (4) 384-400.
[Article ].
Minimizing the Probability of Ruin when Consumption is Ratcheted (with Virginia R. Young), NAAJ, 2008, 12 (4) 428-442.
[Article].
Mutual Fund Theorems when Minimizing the Probability of Lifetime Ruin (with Virginia R. Young), Finance and Research Letters, (2008), 5 (2), 69-78.
[ArXiv], [Article].
Pricing Options in Incomplete Equity Markets via the Instantaneous Sharpe Ratio (with V. R. Young),
Annals of Finance, Volume 4 (4), 399-429 (2008). [ArXiv], [Article].
An Analysis of Monotone Follower Problems for Diffusion Processes,
(with Masa Egami), Mathematics of Operations Research, 33 (2), May 2008, 336-350. [ArXiv], [Article].
Optimal Time To Change Premiums , (with H. Vincent Poor), Mathematical Methods of
Operations Research, 2008, 68 (1), 125-158.[ArXiv], [Article].
Optimizing Venture Capital Investments in a Jump Diffusion Model, (with Masahiko Egami), Mathematical Methods of
Operations Research, 2008, 67 (1), 21-42.
[ ArXiv], [ Article].
Correspondence between Lifetime Minimum Wealth
and Utility of Consumption, (with Virginia R. Young), Finance and Stochastics , 2007, Volume 11 (2)
213-236. [SSRN ]
[ArXiv ], [Article].
The effects of implementation delay on decision-making under uncertainty , (with Masahiko Egami),
Stochastic Processes and Their Applications, 2007, Volume 117 (3), 333-358. [ArXiv], [Article].
Minimizing the Probability of Lifetime Ruin under Borrowing Constraints, (with Virginia R. Young),
Insurance: Mathematics and Economics,, 2007, 41: 196-221 .
[ArXiv], [Article].
Quickest Detection of a Minimum of Two Poisson Disorder Times (with H. Vincent Poor),
SIAM Journal on Control and Optimization, 2007, 46 (1), 308-331.
[ArXiv], [Article].
Hedging Life Insurance: with Pure Endowments , (with V. R. Young),
Insurance: Mathematics and Economics , (2007), Volume 40 (3), 435-444. [ Article].
Adaptive Poisson Disorder Problem, (with Savas Dayanik and Ioannis Karatzas),
Annals of Applied Probability, 16, no. 3 (2006), 1190-1261.
[ ArXiv, Article].
A limit Theorem for Financial Markets with Inert Investors (with Ulrich Horst and Ronnie Sircar),
Mathematics of Operations Research, 2006, Volume 31 (4), 789-810.
[SSRN],
[ArXiv], [Article].
Projecting the Forward Rate Flow onto a Finite Dimensional Manifold, (with H. Vincent Poor and Li Chen), International Journal of
Theoretical and Applied Finance , 2006, Volume 5, 777-785. [ArXiv], [Article].
Stochastic Differential Games in a Non-Markovian Setting (with H. Vincent Poor), SIAM Journal on Control
and Optimization, 2005, Volume 43 (5), 1737-1756.
[ArXiv], [Article].
Standard Poisson Disorder Problem Revisited, (with Savas Dayanik and Ioannis Karatzas),
Stochastic Processes and Their Applications, 2005, 115 (9), 1437-1450.
[ PDF ], [ Article].
Consistency Problems for Jump-Diffusion Models
(with Li Chen and H. Vincent Poor), Applied Mathematical Finance, 2005,
Volume 12 (2), 101-119. [ ArXiv], [ Article].
Arbitrage in Fractal Modulated Markets When the Volatility is Stochastic (with H. Vincent Poor),
International Journal of Theoretical and Applied Finance, Volume 8 (3), 1-18 2005. [ArXiv], [Article].
Prediction and Tracking of Long Range Dependent Sequences, (with H. Vincent Poor and Raghuveer Rao),
Systems and Control Letters, 2005, 54 (11), 1083-1090. [Article].
Estimating the Fractal Dimension of the S&P 500 Index Using Wavelet Analysis (with
with H. Vincent Poor and Ronnie Sircar), International Journal of theoretical and Applied Finance, Volume 7 (5), 613-643,
2004.
[SSRN]
[ArXiv], [Article].
Preprints
A numerical scheme for a mean field game in some queueing systems based on Markov chain approximation method, with Amarjit Budhiraja and Asaf Cohen. [ArXiv].
Multi-Chart Detection Procedure for Bayesian Quickest Change-Point Detection with Unknown
Post-Change Parameters, with Jun Geng and Lifeng Lai. [ArXiv].
Dynamic Programming Principles for Optimal Stopping with Expectation Constraint, with Song Yao. [ArXiv].
Analysis of a Finite State Many Player Game Using its Master Equation, with Asaf Cohen. [SSRN], [ArXiv].
Path-dependent Hamilton-Jacobi equations in infinite dimensions, with Christian Keller. [ArXiv].
Controlled Reflected SDEs and Neumann Problem for Backward SPDEs, with Jinniao Qiu. [ArXiv].
Mini-Flash Crashes, Model Risk, and Optimal Execution, with Alexander Munk. [SSRN], [News Article].
Convergence of approximation schemes for weakly nonlocal second order equations, with Parsiad Azimzadeh and George Labahn. [ArXiv].
Recombining Tree Approximations for Optimal Stopping for Diffusions, with Yan Dolinsky and Jia Guo. [SSRN], [ArXiv].
Arbitrage and hedging with liquid American options, with Zhou Zhou, [SSRN], [ArXiv].
Optimal Investment with Random Endowments and Transaction Costs: Duality Theory and Shadow Prices, with Xiang Yu, [SSRN], [ArXiv].
Efficient Estimation of the Hurst Parameter in High Frequency Financial Data with Seasonalities Using Wavelets,
Proceedings of 2003 International Conference on Computational Intelligence for Financial Engineering (CIFEr2003), Hong-Kong, March 21-25, 2003, [Article].
Prediction and Tracking of Long Range Dependent Sequences Proceedings of the 38th Annual Conference on Information Sciences and Systems, March 2004, Princeton.
Signal Processing Models for Discrete-Time Self-Similar and Multifractal Processes, Proceedings of the 37th Asilomar Conference on Signals, Systems and Computers, Nov 2003, California. [Article].
Quickest Detection of a Minimum of Disorder Times, invited to the 44th IEEE Conference on Decision and Control and
European Control Conference ECC 2005, Seville, December 12-15. [Article].
Multi-source Change Detection for Compound Poisson Processes , Proceedings of 43th Annual Allerton Conference on Communication,
Control, and Computing, September 28-30, 2005.
Quickest Change Point Detection with Sampling Right Constraints, with Jun Geng and Lifeng Lai, Proceedings of the 50th Allerton Conference on Communication, Control, and Computing, October 2012.
Invited Minisymposium (organized by George Yin and Jiongmin Yong) speaker at the SIAM Control Conference on Control and its applications, Pittsburgh, July 10-12,2017.
Mathematical Finance and Partial Differential Equations Conference 2010 at Rutgers University, December 10, 2010 (Invited Speaker).
Ohio State Math Colloquium, December 3, 2010.
SIAM Conference on Financial Mathematics and Engineering (FM10) November 19-20, 2010, San Francisco, plenary speaker and organizer of a session on optimal stopping.
Risk Seminar, Joint seminar of Columbia Statistics and CUNY Graduate Center Math. Nov 5, 2010.
Annual AMS Meeting, San Diego, January 2008 (invited speaker).
Fields Institute, Actuarial Science and Mathematical Finance Group Meeting, Toronto, November 2007 (colloquium talk).
Illinois Institute of Technology, Department of Mathematics, Chicago, November 2007 (colloquium talk).
Financial Mathematics Seminar, University of Texas at Austin, October 12, 2007 (colloquium talk).
The Fourth IASTED International Conference on Financial Engineering and Applications, Berkeley, September 24-26, 2007 (invited speaker).
The 32nd Conference on Stochastic Processes and their Applications, Urbana-Champaign, August 2007 (invited speaker).
Applied Mathematics Institute, Middle East Technical University, Ankara, Aug 2, 2007 (colloquium talk).
Joint Mathematics Colloquium of Bogazici University and Koc University, Istanbul, July 20, 2007.
INFORMS International, Puerto Rico, July 2007 (invited speaker).
Kent-Purdue Minisyposium on Financial Mathematics, April 27-28, 2007 (invited speaker).
Statistics Colloquium, University of Michigan, March 23, 2007.
Whitman School of Management, Syracuse University, Finance Colloquium, March 2, 2007 (colloquium talk).
Dept. of Mathematics, Mathematics Bowling Green State University, February 23, 2007 (colloquium talk).
University of Florida, Dept. of Industrial Engineering, February 9, 2007 (colloquium talk).
Probability Seminar, Mathematical Sciences, Carnegie Mellon University, January 15, 2007 (colloquium talk).
Annual AMS Meeting, January 5-8, 2007 (invited speaker).
Probability Seminar, Columbia University, Department of Mathematics, Dec. 15 2006 (colloquium talk).
Probability and Mathematical Finance Seminar, Carnegie Mellon University, Department of Mathematical Sciences, November 20, 2006 (colloquium talk).
Informs Annual Meeting, Pittsburgh, November 5-8, 2006 (invited speaker for the Financial Engineering Session).
SIAM Conference on Financial Mathematics and Engineering, July 9-12, Boston, (invited speaker).
21st European Conference on Operations Research in Reykjavik, Iceland, July 2-5, (invited speaker).
Operations Management Colloquium, University of Michigan, Stephen M. Ross School of Business, March 3, 2006, (colloquium talk).
Industrial Engineering and Operations Research, University of California at Berkeley, Feb 24, 2006, (colloquium talk).
Industrial Engineering and Operations Research, Columbia University, Feb 22, 2006, (colloquium talk).
Statistics, University of California at Berkeley, February 7, 2006, (colloquium talk).
Mathematics, Illinois Institute of Technology, January 30, 2006, (colloquium talk).
Statistics and Operations Research, University of North Carolina at Chapel Hill, January 27, 2006, (colloquium talk).
Industrial Engineering, Industrial and Enterprise Systems Engineering, University of Illlinois at Urbana Champaign, January 23, 2006, (colloquium talk).
Applied Probability and Statistics, University of California at Santa Barbara, January 20, 2006, (colloquium talk).
Industrial Engineering Special Seminar, Purdue University, December 6, 2005, (colloquium talk).
Informs Annual Meeting, San Fransisco, November 13-16, 2005 (invited speaker for the Financial Engineering Session).
Financial/ Actuarial Mathematics Seminar, University of Michigan, Dept. of Mathematics, September 15, 2005.
CMS Summer Meeting, Waterloo, CA, June, 2005 (invited speaker to the Mathematics of Actuarial Finance session).
Stochastic Analysis Seminar, Princeton University, March 30, 2005.
Financial/ Actuarial Mathematics Seminar, University of Michigan, Dept. of Mathematics, February 17, 2005.
Financial/ Actuarial Mathematics Seminar, University of Michigan, Dept. of Mathematics, November 4, 2004.
Informs Annual Meeting, Denver, October 24-27, 2004 (invited speaker for the Financial Engineering Session).
Third World Congress of the Bachelier Finance Society, Chicago, July 21-24, 2004.
Industrial and Systems Engineering, University of Florida, Dept. of Industrial Engineering, February 12, 2004, (colloquium talk).
Mathematics, Florida State University, Dept. of Mathematics, Feb 02, 2004, (colloquium talk).
Fractional Brownian Days, Helsinki, Finland, September 26-27, 2003.
29th Conference on Stochastic Processes and Their Applications, Angra dos Reis, Brazil, August 3 - 9, 2003.
Euro Informs Joint International Meeting, Istanbul,Turkey, July 6-10, 2003;
Eighth Viennese Workshop on Optimal Control, Dynamic Games and Nonlinear Dynamics, Vienna,May 14-16, 2003.
Collaborators
Bahman Angoshtari (University of Washington, Department of Applied Mathematics).
Parsiad Azimzadeh (University of Waterloo, Department of Computer Science).
Nicole Bauerle (Karlsruhe Institute of Technology, Department of Mathematics, Germany).
Amarjit Budhiraja (The University of North Carolina at Chapel Hill, Department of Statistics and Operations Research).
Bo Yang , Executive Director, Morgan Stanley. Defended on August 13, 2008. [ Thesis ]
Hao Xing , Associate Professor@ the Statistics Department of the London School of Economics. Defended on the 20th of April, 2009. [ Thesis ]
Xueying Hu , Vice President, Market risk modeling, Goldman Sachs. Defended on the 6th of January, 2012. [ Thesis ]
Ross Kravitz , Senior Data Scientist at Pandora. Defended on the 10th of January 2013. [ Thesis ]
Yu-Jui Huang , Assistant Professor, Department of Applied Mathematics, University of Colorado Boulder. Defended on April 30th, 2013. [ Thesis ]
Yuchong Zhang (Defended on March 31, 2015; Term Assistant professor at Columbia University 2015-2018; tenure track assistant professor at the University of Toronto, Department of Statistics starting May 2018).[ Thesis ]
Zhou Zhou (Defended on April 1, 2015; IMA post-doc 2015-2017; Post-doc at University of Michigan Fall 2017; Tenure track assistant professor at the University of Sydney starting January 2018). [ Thesis ]
Jiaqi Li (Defended on August 16, 2016; Associate, Controller modeling, Goldman Sachs). [ Thesis ]
Alex Munk (Defended on May 31, 2017; Financial Engineer at Chicago Trading Company). [ Thesis ]