Stochastic optimization with applications in finance, insurance and engineering; optimal control;
singular stochastic control; optimal stopping; quickest change point detection.
Stochastic process limits for processes with semi-Markov switching; stochastic calculus for fractional Brownian motion; stochastic differential games; estimation techniques for long range dependent processes.
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)
Journal Articles
Pricing Options on Defaultable Stocks, Applied Mathematical Finance , (2008), Volume 15 (3).
[ PDF ], [Arxiv ]
Pricing Options in Incomplete Equity Markets via the Instantaneous Sharpe Ratio (with V. R. Young),
to appear in Annals of Finance, (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 ]
Optimizing Venture Capital Investments in a Jump Diffusion Model, (with Masahiko Egami), Mathematical Methods of
Operations Research, 2008, 67 (1), 21-42.
[ PDF]
Optimal Time To Change Premiums , (with H. Vincent Poor), to appear in the Mathematical Methods of
Operations Research.[ 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), 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),
2004. [ 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.
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, 2006 (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.