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 Applied Mathematics Research Grant, DMS-0906257, 2009-2012 (PI).
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)
Journal Articles
On the One-Dimensional Optimal Switching Problem , (with Masahiko Egami), to appear in Mathematics of Operations Research [ PDF ]
Optimal Trade Execution in Illiquid Markets, (with Mike Ludkovski), to appear in Mathematical Finance. [ PDF]
A Unified Framework for Pricing Credit and Equity Derivatives (with Bo Yang), to appear in Mathematical Finance. [ PDF ]
Pricing Asian Options for Jump Diffusions
(with Hao Xing), to appear in Mathematical Finance [PDF ]
Inventory Management with Partially Observed Non-stationary Demand
(with Mike Ludkovski), to appear in Annals of Operations Research [PDF ]
Optimal investment strategy to minimize occupation time (with Jenny Young), to appear in Annals
of Operations Research [PDF ]
On the Perpetual American Put Options for Level Dependent Volatility Models with Jumps, to appear in Quantitative Finance [ PDF ]
On the Stickiness Property, (with Hasanjan Sayit), to appear in Quantitative Finance [ PDF ]
A Unified Treatment of Dividend Payment Problems under Fixed Cost and Implementation Delays,
(with Masa Egami), to appear in Mathematical Methods of Operations Research [ 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), 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 ]
Preprints
Optimal Stopping for Dynamic Convex Risk Measures, with Ioannis Karatzas and Song Yao. [ PDF]
On the Existence of Consistent Price Systems, with Hasanjan Sayit. [ PDF]
Strict Local Martingale Deflators and Pricing American Call-Type Options, with Constantinos Kardaras and Hao Xing. [ PDF ]
On the uniqueness of classical solutions of Cauchy problems, with Hao Xing. [ PDF ]
On the Continuity of Stochastic Exit Time Control Problems, with Qingshuo Song and Jie Yang. [ PDF ]
Optimal Stopping for Nonlinear Expectations, with Song Yao. [ PDF ]
Regularity of the Optimal Stopping Problem for Levy Processes with Non-Degenerate Diffusions, with Hao Xing. [ PDF ]
Proving the Regularity of the Minimal Probability of Ruin via a Game of Stopping and Control, with Virginia R. Young. [ 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.
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).
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)
Mike Ludkovski (University of California at Santa Barbara, Department of Applied Probability and Statistics).
Moshe Milevsky (York University, Schulich School of Business).
Kristen Moore (University of Michigan, Department of Mathematics).
H. Vincent Poor (Princeton University, School of Engineering and Applied Science), My Ph.D Advisor.
David Promislow (York University, Department of Mathematics and Statistics).
Raghuveer Rao (Rochester Institute of Technology, Department of Electrical Engineering).
Hasanjan Sayit (Worcester Polytechnic Institute, Department of Mathematics).
Semih Sezer (Sabanci University, Department of Industrial Engineering).
Ronnie Sircar (Princeton University, Department of Operations Research and Financial Engineering).
Qingshuo Song (University of Michigan, Department of Mathematics).
Song Yao (University of Michigan, Department of Mathematics).