National Science Foundation CAREER Grant in Applied Mathematics, DMS-0955463, 2010-2015 (PI).
National Science Foundation, Division of Mathematical Sciences, Computational Foundations for Emerging Science Frontiers, DMS-1118673, 2011-2014 (PI, joint with Lifeng Lai and H. Vincent Poor).
National Science Foundation Applied Mathematics Research Grant, DMS-0906257, 2009-2012 (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)
SIAM Activity Group on Financial Mathematics and Engineering (SIAG/FME) (the inaugural) Junior Scientist Prize 2010.
Journal Articles (Below are the links to the versions on ArXiv. For the official versions please visit the journals' websites. )
Stochastic Perron's method and verification without smoothness using viscosity comparison: obstacle problems and Dynkin games, (with Mihai Sirbu), to appear in the Proceedings of the American Mathematical Society . [PDF]
Regularity of the Optimal Stopping Problem for Jump Diffusions, (with Hao Xing), to appear in SIAM Journal on Control and Optimization. [ PDF ]
Liquidation in Limit Order Books with Controlled Intensity, (with Mike Ludkovski), to appear in Mathematical Finance [PDF
]
Outperforming the Market Portfolio with a Given Probability, (with Yu-Jui Huang and Qingshuo Song), to appear in the Annals of Applied Probability . [PDF ]
Stochastic Perron's method and verification without smoothness using viscosity comparison: the linear case, (with Mihai Sirbu), to appear in the Proceedings of the American Mathematical Society . [PDF
]
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. [ PDF]
Valuation equations for stochastic volatility models, (with Kostas Kardaras and Hao Xing), SIAM Journal on Financial Mathematics, 2012, 3, 351-373. [PDF ]
Strict Local Martingale Deflators and Pricing American Call-Type Options, (with Constantinos Kardaras and Hao Xing), Finance and Stochastics , (2012), 16(2), 275-291. [ PDF ]
Quadratic Reflected BSDEs with Unbounded Obstacles, (with Song Yao), Stochastic Processes and Their Applications, (2012), 122, 1155-1203. [PDF ]
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 [ PDF ]
Optimal Trade Execution in Illiquid Markets, (with Mike Ludkovski), Mathematical Finance (2011), 21(4), 681-701.[ PDF]
A Unified Framework for Pricing Credit and Equity Derivatives (with Bo Yang), Mathematical Finance, (2011), 21 (3), 493-517. [ PDF ]
On the Perpetual American Put Options for Level Dependent Volatility Models with Jumps, Quantitative Finance, (2011), 335-341. [ PDF ]
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. [PDF ]
Optimal Stopping for Nonlinear Expectations, Part I (with Song Yao), Stochastic Processes and Their Applications (2011), 121 (2), 185-211.
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 [ PDF ]
Pricing Asian Options for Jump Diffusions
(with Hao Xing), Mathematical Finance (2011), 21 (1), 117-143. [PDF ]
On the Continuity of Stochastic Exit Time Control Problems, (with Qingshuo Song and Jie Yang), Stochastic Analysis and Applications (2011), 29, 1-13. [ PDF ]
On the Stickiness Property, (with Hasanjan Sayit), Quantitative Finance, (2010), 10 (10), 1109-1112. [ PDF ]
On the uniqueness of classical solutions of Cauchy problems, (with Hao Xing), Proceedings of the American Mathematical Society, (2010), 138 (6), 2061-2064. [ PDF ]
On the One-Dimensional Optimal Switching Problem , (with Masahiko Egami), Mathematics of Operations Research, 2010, 35 (1), 140-159. [ PDF ]
Inventory Management with Partially Observed Non-stationary Demand
(with Mike Ludkovski), Annals of Operations Research, 2010, 176 (1), 7-39. [PDF ]
Optimal investment strategy to minimize occupation time (with Jenny Young), Annals
of Operations Research, 2010, 176 (1), 389-408. [PDF ]
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. [ PDF ]
No Arbitrage Conditions For Simple Trading Strategies (with Hasanjan Sayit), Annals of Finance, (2010), 6 (1), 147-156. [PDF ]
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. [PDF ]
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. [PDF ]
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.
[PDF ]
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.
[PDF ]
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.
[PDF ]
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. [An older version with a different title]
Optimal Deferred Life Annuities to Minimize the Probability of Lifetime Ruin (with Jenny Young), NAAJ, (2009) 13 (1), 141-154. [PDF ]
Relative Hedging of Systematic Mortality Risk (with Mike Ludkovski), NAAJ, (2009), 13 (1), 106-140. [PDF ]
Minimizing the Lifetime Shortfall or Shortfall at Death (with Jenny Young), Insurance: Mathematics and Economics, 2009, 44 (3), 447-458. [PDF ]
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.
[PDF ]
Minimizing the Probability of Lifetime Ruin under Random Consumption (with Kristen Moore and Virginia R. Young), NAAJ, 2008, 12 (4) 384-400.
[PDF ]
Minimizing the Probability of Ruin when Consumption is Ratcheted (with Virginia R. Young), NAAJ, 2008, 12 (4) 428-442.
[PDF ]
Mutual Fund Theorems when Minimizing the Probability of Lifetime Ruin (with Virginia R. Young), Finance and Research Letters, (2008), 5 (2), 69-78.
[PDF ]
Pricing Options in Incomplete Equity Markets via the Instantaneous Sharpe Ratio (with V. R. Young),
Annals of Finance, Volume 4 (4), 399-429 (2008)
[ PDF ]
An Analysis of Monotone Follower Problems for Diffusion Processes,
(with Masa Egami), Mathematics of Operations Research, 33 (2), May 2008, 336-350 [ PDF ]
Optimal Time To Change Premiums , (with H. Vincent Poor), Mathematical Methods of
Operations Research, 2008, 68 (1), 125-158.[ PDF]
Optimizing Venture Capital Investments in a Jump Diffusion Model, (with Masahiko Egami), Mathematical Methods of
Operations Research, 2008, 67 (1), 21-42.
[ PDF]
Correspondence between Lifetime Minimum Wealth
and Utility of Consumption, (with Virginia R. Young), Finance and Stochastics , 2007, Volume 11 (2)
213-236. [PDF ]
The effects of implementation delay on decision-making under uncertainty , (with Masahiko Egami),
Stochastic Processes and Their Applications, 2007, Volume 117 (3), 333-358. [ PDF ]
Minimizing the Probability of Lifetime Ruin under Borrowing Constraints, (with Virginia R. Young),
Insurance: Mathematics and Economics,, 2007, 41: 196-221 .
[ PDF ]
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.
[ PDF ]
Hedging Life Insurance: with Pure Endowments , (with V. R. Young),
Insurance: Mathematics and Economics , (2007), Volume 40 (3), 435-444. [ PDF ]
Adaptive Poisson Disorder Problem, (with Savas Dayanik and Ioannis Karatzas),
Annals of Applied Probability, 16, no. 3 (2006), 1190-1261.
[ PDF ]
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. [ PDF ]
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. [ PDF ]
Stochastic Differential Games in a Non-Markovian Setting (with H. Vincent Poor), SIAM Journal on Control
and Optimization, 2005, Volume 43 (5), 1737-1756.
[ PDF ], or [PDF ]
Standard Poisson Disorder Problem Revisited, (with Savas Dayanik and Ioannis Karatzas),
Stochastic Processes and Their Applications, 2005, 115 (9), 1437-1450.
[ PDF ]
Consistency Problems for Jump-Diffusion Models
(with Li Chen and H. Vincent Poor), Applied Mathematical Finance, 2005,
Volume 12 (2), 101-119. [ PDF ]
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. [ PDF ]
Prediction and Tracking of Long Range Dependent Sequences, (with H. Vincent Poor and Raghuveer Rao),
Systems and Control Letters, 2005, 54 (11), 1083-1090
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. [ PDF ]
Preprints
On the Impulse Control of Jump Diffusions, with Tom Emmerling and Jose-Luis Menaldi. [PDF]
Quickest Search over Brownian Channels, with Ross Kravitz. [PDF]
On Zero-Sum Stochastic Differential Games, with Song Yao. [PDF]
A Stochastic Approximation for Fully Nonlinear Free Boundary Problems, with Arash Fahim. [PDF]
Robust maximization of asymptotic growth under covariance uncertainty, with Yu-Jui Huang. [PDF
]
Stability of exponential utility maximization with respect to market perturbations, with Ross Kravitz. [PDF
]
On the Multi-dimensional controller and stopper games, with Yu-Jui Huang. [ PDF]
On the Existence of Consistent Price Systems, with Hasanjan Sayit. [ PDF]
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.
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.
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.
Multi-source Change Detection for Compund Poisson Processes , Proceedings of 43th Annual Allerton Conference on Communication,
Control, and Computing, September 28-30, 2005.
Financial Mathematics Seminar, ETH, Zurich, May 10.
Finance and Stochastics Seminar, Imperial College, Department of Mathematics, March 14, 2012.
Actuarial and Financial Mathematics Conference, Brussels, February 9-12, 2012. (Plenary speaker.)
Mathematics Colloquium, University of Minnesota, Dec 1, 2011.
Workshop on Liquidity Risk Modeling, organized by the University of Evry, Nov 18-19, 2011, Paris. (Plenary speaker.)
Mathematical Finance Seminar, University of Evry, Nov 17, 2011.
Mathematics Colloquium, University of Sydney, Nov 4th, 2011.
Mathematical Finance Colloquium, USC, Oct 17, 2011.
Mathematics Colloquium, Rutgers University, September 16.
Economics Colloquium, Rutgers University, September 15.
International Conference on Mathematical Finance and Economics, Istanbul, July 6-8 (Plenary speaker).
The 35th Conference on Stochastic Processes and their Applications, Oaxaca, Mexico, 19th-24th of June (Invited speaker).
6th Symposium on BSDEs and Applications, University of Southern California (USC), June 8-10, 2011 (Invited Speaker).
Advances in Portfolio Theory and Investment Management, Oxford-Man Institute, University of Oxford, May 12, 13 and 14, 2011 (keynote speaker).
Risk & Stochastics Seminar, London School of Economics, May 11, 2011.
Bachelier Seminar, l'Institut Henri Poincare, Paris, France, May 6.
Mathematical Finance Seminar, Paris 6 and 7, France, May 5.
Mathematics Colloquium, Wayne State University, April 18.
Inaugural lecture for the Susan M. Smith Chair, University of Michigan, March 22.
Cornell ORIE Colloquium, January 25, 2011.
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.
Financial Mathematics Seminar, University of Texas at Austin, April 23, 2010.
Western Michigan University, Mathematics Colloquium, March 18, 2010.
Montreal Seminar of Actuarial and Financial Mathematics, March 12, 2010.
Center for Research in Financial Mathematics and Statistics (seminar), UCSB, February 22, 2010.
Cornell University, Probability Seminar, October 19, 2009.
INFORMS Annual Meeting, Oct 11-14, 2009. (Invited to the Credit Portfolio Optimization, Finance and Stochastics Sessions.)
Rutgers University, Mathematical Finance and Probability Seminar, September 29, 2009.
Georgia State University, Department of Risk Management and Insurance, Quantitative Finance Seminar, August 28, 2009.
Stanford University, Department of Mathematics, Financial Mathematics Seminar, April 24, 2009.
Fields Institute Quantitative Finance Seminar Series, April 2, 2009 (colloquium speaker).
University of Southern California, Dept. of Mathematics, Mathematical Finance Colloquium. Feb 23, 2009.
Princeton University, Stochastic Analysis Seminar, 16th and 18th of February, 2009.
AMS Annual Meeting, Special Session on Financial Mathematics, Washington D.C., Jan. 7-8, 2009 (Co-organizer)
SIAM Conference on Financial Mathematics and Engineering, Rutgers, November 21-22, 2008 (invited speaker)
Probability Seminar, Columbia University, Department of Mathematics, November 14, 2008 (colloquium).
IFID/MITACS Conference on Financial Engineering for Actuarial Mathematics, Fields Institute, Toronto (November 9-10, 2008) (keynote speaker)
Istanbul Center for Mathematical Sciences, May 2008 (colloquium talk).
Workshop
in Memory
of Professor Hayri Korezlioglu, Ankara, Turkey, April 2008 (keynote speaker).
Daiwa Young Researchers' Intenational Workshop, March 2008, Kyoto University, Japan (keynote speaker).
Oberwolfach Workshop on Stochastic Analysis in Finance and Insurance, Germany, January 2008.
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, Janury 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
Li Chen (Merrill Lynch).
Savas Dayanik (Bilkent University, Department of Industrial Engineering).
Masahiko Egami (Kyoto University, Graduate School of Economics).
Tom Emmerling
(University of Michigan, Department of Mathematics).
Arash Fahim
(University of Michigan, Department of Mathematics).
Ulrich Horst (Humboldt University of Berlin, Department of Mathematics).
Ioannis Karatzas (Columbia University, Department of Mathematics),
Kostas Kardaras (Boston University, Department of Mathematics and Statistics).
Lifeng Lai (University of Arkansas, Little Rock, Department of Systems Engineering).
Mike Ludkovski (University of California at Santa Barbara, Department of Applied Probability and Statistics).