Department of Mathematics University of Michigan |
Office:Email: |
2846 East Hallerhan [no spam] umich (dot) edu |

- (Full) Professor, Sep 2013 onwards, Department of Mathematics, University of Michigan.
- Director of the Quantitative Finance and Risk Management Masters Program, January 2015 onwards.
- Associate Professor (with Tenure), Sep 2010-August 2013, Department of Mathematics, University of Michigan.
- Assistant Professor (Tenure Track), Sep 2006-August 2010, Department of Mathematics, University of Michigan.
- T. H. Hildebrandt Research Assistant Professor, Aug 2004-Aug 2006, Department of Mathematics, University of Michigan.

- Ph.D., Princeton University, 2004.
- M.A., Princeton University, 2002.
- B.S., Electrical Engineering (Alumni in academia ), Middle East Technical University, Turkey, 2000.
- B.S. Mathematics, Middle East Technical University, Turkey, 2000.
- Science High School of Izmir (Izmir Fen Lisesi) , Turkey, 1996.

- Probability and Random Processes II, MATH/STAT 626: Winter 2008, Winter 2009, Winter 2012, Winter 2013, Winter 2015, Winter 2017.

- Probability and Random Processes I, MATH/STAT 625, Winter 2007, Fall 2007, Fall 2008, Fall 2011, Fall 2013, Fall 2014, Fall 2017.

- Computational Finance, MATH/IOE 623: Fall 2004, Winter 2005, Winter 2006, Fall 2006, Fall 2010, Winter 2011, Fall 2015.

- Discrete State Stochastic Processes, MATH/STAT 526: Fall 2008, Fall 2016.
- Continuous Time Stochastic Analysis for Finance, Math 506: Fall 2007.

- Mathematical Finance, MATH 423: Fall 2005, Winter 2012, Winter 2013.

- Mathematical finance, applied probability, stochastic analysis, stochastic control, optimal stopping.

*Topics in Stochastic Processes and Their Applications*, Princeton University 2004. [ Link ]

- 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).

- Susan M. Smith Professorship, 2010-.
- SIAM Activity Group on Financial Mathematics and Engineering (SIAG/FME) (the inaugural) Early Career Prize, 2010.

- Associate Editor of Applied Mathematics and Optimization, July 2016-December 2018.
- Associate Editor of Mathematical Finance, November 2013-.
- Associate Editor of Mathematics of Operations Research, December 2013- December 2018.
- Associate editor of SIAM Journal on Control and Optimization (SICON), January 2014-.

*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]. -
*Risk Sensitive Control of the Lifetime Ruin Problem*, (with Asaf Cohen), to appear in**Applied Mathematics and Optimization**, [SSRN], [ArXiv], [Article].

*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].*Multi-scale Time- Changed Birth Processes for Pricing Multi-Name Credit Derivatives*(with Bo Yang),**Applied Mathematical Finance,**(2009), 16 (5), 429-449. [PDF ], [SSRN], [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 on Defaultable Stocks*,**Applied Mathematical Finance**, (2008), Volume 15 (3), 277-304. [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].*Queuing theoretic approaches to financial price fluctuations*(with Ulrich Horst and Ronnie Sircar), [SSRN],**Handbooks in OR&MS: Financial Engineering, 15, eds. John Birge and Vadim Linetsky, (Elsevier)**, (2008) [ArXiv], [Google books].*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].*Poisson Disorder Problem with Exponential Penalty for Delay*, (with Savas Dayanik),**Mathematics of Operations Research**, 31:2, 217-233, 2006; finalist in INFORMS 2004 Junior Faculty Interest Group Paper Competition. [ PDF], [ Abstract].*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].

- 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].
- Solvability of the non-linear Dirichlet problem with jumps, with Qingshuo Song. [ArXiv].
- 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].
- Martingale optimal transport with stopping, with Alex Cox and Yavor Stoev, [SSRN], [ArXiv].
- On the controller-stopper problems with controlled jumps, with Jiaqi Li, [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. -
*Pricing American Options for Jump Diffusions with Iterated SOR*, Proceeding of Financial Engineering and Applications - 2007 *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.
- Invited speaker at Robust Methods in Probability and Finance, ICERM, Brown University, June 19-23, 2017.
- Colloquium at LUISS, Departimento Economia and Finanza, Rome, Italy, May 19, 2017.
- de Finetti Risk Seminar , May 17, Milano, Italy.
- Probability and Computational Finance Seminars, Carnegie Mellon, May 1, 2017.
- Quantitative Finance Seminar, Fields Institute , University Toronto, April 26, 2017.
- Special Invited Lecture at the 16th Winter school on Mathematical Finance, Netherlands, January 2017.
- Invited mini-symposium speaker at SIAM Conference on Financial Mathematics and Engineering, November 17-19, 2016, Austin, TX.
- Plenary speaker at the 9th World Congress of the Bachelier Finance Society, July 15-19, 2016.
- HPV65 A Workshop Honoring Vince Poor, July 9, 2016.
- Invited speaker at 2016 Risk and Stochastics Conference, London School of Economics, April 2016.
- Invited speaker at 1st Eastern Conference on Mathematical Finance, Worcester, MA, March 2016.
- Princeton, ORFE Colloquium, October 6, 2015.
- Georgia Tech, ISyE Colloquium, September 16, 2015.
- Invited speaker in the Stochastic Control Session at the AMS Sectional Meeting at Michigan State University in East Lansing, Michigan, 3,1415.
- Invited speaker at the Paris-Southeast Asia Conference in Mathematical Finance, February 7-11, Siem Reap, Cambodia.
- Plenary speaker at the NUS-University of Paris Diderot Workshop in Quantitative Finance, February 4-5, 2015, Singapore.
- Boeing Distinguished Colloquium, University of Washington, Nov 20, 2014.
- Mini symposium speaker at SIAM Meeting on Financial Math, Nov 13-15, 2014, Chicago. (Also a member of the organizing committee.)
- Invited speaker at Trading and Portfolio Theory, November 11-12, 2014, University of Chicago.
- Financial Mathematics Seminar, Princeton University, September 11, 2014.
- New Directions in Financial Mathematics and Mathematical Economics, Banff, CA, July 6-11, 2014.
- Plenary talk at Labex Louis Bachelier - SIAM-SMAI Conference on Financial Mathematics: Advanced Modeling and Numerical Methods, June 17-20, 2014, Paris.
- Colloquium of ISFA (Institut de Science Financiere et d'Assurances), University of Lyon 1, June 4, 2014.
- Financial Math Colloquium, Department of Mathematical Sciences, Dublin City University, May 28, 2014.
- Stochastic Analysis in Finance and Insurance. Mathematisches Forschungsinstitut Oberwolfach, Germany, May 4-10, 2014.
- Columbia Mathematical Finance Seminar, March 6, 2014.
- Scoping Meeting on Mathematical and Physical Sciences of Modern Financial Markets: Computerised Trading at Low and High Frequency, Isaac Newton Institute, Cambridge, 19-21 November 2013.
- Probability and Statistics seminar, Universite du Maine (Laboratoire Manceau de Mathematiques), October 8, 2013.
- Financial Mathematics Seminar, University of Pittsburgh , Feb 11, 2013.
- Mathematics Colloquium, WPI, December 7, 2012.
- Statistics and Probability Seminar series, Boston University, December 6, 2012.
- 2012 Algorithm Workshop (organized by NSF), November 26-29, 2012. in San Diego, CA.
- Financial and Insurance Mathematics Seminar, Nov 6, 2012, ETH, Zurich.
- Plenary speaker at the International Conference on Advanced Stochastic Optimization Problems organized by the Steklov Institute of Math, Moscow, September 24-28 (keynote speaker).
- Math Finance Colloquium, USC, September 17, 2012.
- Probability, Control and Finance: A Conference in Honor of the 60th Birthday of Ioannis Karatzas, June 4-8, 2012, NYC. (Plenary speaker.)
- Mathematical Finance Seminar, University of Evry, Dept. of Math, May 31, 2012, France.
- Financial Mathematics Seminar, ETH, Zurich, May 10, 2012.
- 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, 2011.
- Economics Colloquium, Rutgers University, September 15, 2011.
- International Conference on Mathematical Finance and Economics, Istanbul, July 6-8 (Plenary speaker), 2011.
- The 35th Conference on Stochastic Processes and their Applications, Oaxaca, Mexico, 19th-24th of June (Invited speaker), 2011.
- 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, 2011.
- Mathematical Finance Seminar, Paris 6 and 7, France, May 5, 2011.
- Mathematics Colloquium, Wayne State University, April 18, 2011.
- Inaugural lecture for the Susan M. Smith Chair , University of Michigan, March 22, 2011.
- 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.
- Bachelier Finance Society World Congress, Fields Institute, Toronto, June 22-26, 2010 (Invited speaker in the Stochastic Control Theme).
- IMA Workshop, New Mathematical Models in Economics and Finance, June 9-18.
- 6th Conference in Actuarial Science & Finance on Samos, June 3-6, 2010 (Keynote speaker).
- 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).
- Stochastic Analysis in Finance and Insurance. Mathematisches Forschungsinstitut Oberwolfach, Germany, Jan 27-Feb 2, 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, 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.

- 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).
- Li Chen (Executive Director, JPMorgan Chase).
- Asaf Cohen (University of Haifa, Department of Statistics).
- Andrea Cosso (Dipartimento di Matematica, Politecnico di Milano).
- Alexander Cox (University of Bath, Department of Mathematical Sciences).
- Savas Dayanik (Bilkent University, Department of Industrial Engineering, Turkey).
- Yan Dolinsky (Hebrew University, Department of Statistics, Israel).
- Masahiko Egami (Kyoto University, Graduate School of Economics, Japan).
- Tom Emmerling (Now Senior Quantitative Risk Analyst at M&T Bank Corporation).
- Arash Fahim (Florida State University, Department of Mathematics).
- Georgios Fellouris (University of Illinois at Urbana-Champaign, Department of Statistics).
- Ulrich Horst (Humboldt University of Berlin, Department of Mathematics).
- Ioannis Karatzas (Columbia University, Department of Mathematics),
- Kostas Kardaras (LSE, Department of Statistics).
- Christian Keller (University of Michigan, Department of Mathematics).
- Andreas Kyprianou (University of Bath, Department of Mathematical Sciences),
- Lifeng Lai (UC Davis, Electrical and Computer Engineering).
- Zhibin Liang (School of Mathematical Sciences, Nanjing Normal University, China).
- Mike Ludkovski (University of California at Santa Barbara, Department of Applied Probability and Statistics).
- Jose-Luis Menaldi (Wayne State University, Department of Mathematics).
- Moshe Milevsky (York University, Schulich School of Business, Canada).
- Christopher W. Miller (Associate at Goldman Sachs).
- Kristen Moore (University of Michigan, Department of Mathematics).
- Sergey Nadtochiy (University of Michigan, Department of Mathematics).
- Mikko Pakkanen (Department of Mathematics, Imperial College, London).
- Huyen Pham (Laboratoire de Probabilites et Modeles Aleatoires, Universite Paris Diderot).
- H. Vincent Poor (Princeton University, School of Engineering and Applied Science), My Ph.D Advisor.
- David Promislow (York University, Department of Mathematics and Statistics, Canada).
- Jinniao Qiu, (University of Calgary, Department of Mathematics and Statistics).
- Raghuveer Rao (Army Research Lab).
- Hasanjan Sayit (Durham University, Department of Mathematical Sciences).
- Semih Sezer (Sabanci University, Department of Industrial Engineering, Turkey).
- Mihai Sirbu (University of Texas at Austin, Department of Mathematics).
- Ronnie Sircar (Princeton University, Department of Operations Research and Financial Engineering).
- Qingshuo Song (City University of Hong Kong, Department of Mathematics).
- Yavor Stoev, (University of Michigan, Department of Mathematics.)
- Gu Wang (WPI, Department of Mathematical Sciences).
- Kazutoshi Yamazaki (Kansai University, Japan).
- Jie Yang (University of Illinois at Chicago, Department of Mathematics).
- Song Yao (University of Pittsburgh, Department of Mathematics).
- Virginia (Jenny) R. Young (University of Michigan, Department of Mathematics).
- Xiang Yu (Hong Kong Polytechnic University, Department of Applied Mathematics).

- 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 ]
- Jia Guo.
- Jingjie Zhang.
- Xin Zhang

- Ronnie Sircar, 1997-2000.

(Now Professor at Princeton University, Department of Operations Research and Financial Engineering). - Yevgeny Goncharov, 2003-2004.

(Now Research Analyst at Quantitative Risk Management, Chicago). - Masahiko Egami, 2005-2007.

(Now Full Professor at Kyoto University, Graduate School of Economics, Japan). - Mike Ludkovski , 2005-2008.

(Now Full Professor at the University of California at Santa Barbara, Department of Applied Probability and Statistics). - Semih Sezer , 2006-2008.

(Now Associate Professor at Sabanci University, Department of Industrial Engineering, Turkey). - Ahmet Duran, 2006-20010.

(Now Associate Professor at Istanbul Technical University, Department of Mathematical Engineering, Turkey). - Song Yao , 2008-2011.

(Now Associate Professor at the University of Pittsburgh, Department of Mathematics). - Qingshuo Song , 2009.

(Now Associate Professor at the City University of Hong Kong, Department of Mathematics). - Tom Emmerling, 2009-2012.

(Senior Quantitative Risk Analyst at M\&T Bank Corporation.) - Jose Alcala Burgos, 2010-2013.

(Now CONACYT fellow at CIMAT, Facultad de Matematicas, Mexico). - Arash Fahim, 2011-2013.

(Now Assistant Professor at Florida State University, Department of Mathematics). - Xiang Yu , 2012-2015.

(Now Tenure track Assistant Professor, Hong Kong Polytechnic University, Department of Applied Mathematics). - Gu Wang, 2013-2015.

(Now Tenure track Assistant Professor at WPI, Department of Mathematical Sciences). - Jinniao Qiu, 2015-2018

(Now Tenure track assistant professor at the University of Calgary, Department of Mathematics and Statistics). - Bahman Angoshtari 2014-2017.

(Now term assistant professor at the University of Washington, Department of Applied Mathematics). - Asaf Cohen, 2014-2017

(Now tenure track assistant professor at the University of Haifa, Department of Statistics). - Christian Keller, 2015-2018.
- Yavor Stoev, 2015-2018.
- Sebastian Hermann, 2016-2019.
- Zhou Zhou, Fall 2017.
- Ibrahim Ekren, 2017-2020.
- Nicolas Hernandez, 2017-2020.
- Alexandros Saplaouras, 2017-2020.

- Erdos Number: 4 (Erdos->Fisburne->Burnashev/Calderbank->Poor->Bayraktar), (Erdos->Berger*/Mauldin->Soner*/Sudderth**->Karatzas* **/ Dolinsky*->Bayraktar), (Erdos->Janson->Protter*/Hobson->Sayit*/Cox->Bayraktar), (Erdos->Diaconis->Follmer->Horst->Bayraktar), (Erdos->Tetali->Ramanan->Budhiraja->Bayraktar), (Erdos->Alon->Kriz->Xing->Bayraktar), (Erdos->Vaaler->Burger->Kravitz->Bayraktar).
- Funding Rank of Mathematicians for 2011
- World Ranking of Universities by Reputation 2016
- Ranking of Math Departments in the US
- Ranking of Applied Math in the US
- University of Michigan Faculty History Project

- Updated on 10.9.17 by Erhan Bayraktar