Research Interests 

•  Stochastic Processes and Stochastic Analysis: Lévy Process; Wiener-Hopf Factorization; Feynman-Kac Formulas; Stochastic Control 

•  Mathematical Finance: Small-Time Asymptotic Expansions of Option Prices, with Emphasis on Lévy-Based Jump-Diffusion Models 

•  Random Sequence Alignments: Limiting Theorems; Asymptotic Moment Estimates; Connections with Random Matrices and Random Percolation 

•  Stochastic Partial Differential Equations: Statistical Inference for SPDEs 

Curriculum Vitae (This version: February 2023) 

Graduate Student 

• Ziteng Cheng, Ph.D. in Applied Mathematics (co-advised with T. R. Bielecki)

Date of Graduation: May 2021

Thesis Topics: Wiener-Hopf Factorizations for Time-Inhomogeneous Markov Processes; Bayesian Estimations for Stochastic Partial Differential Equations 

Next Position: Postdoc Fellow, Department of Statistical Sciences, University of Toronto, Toronto, ON, Canada

Publications & Preprints 

• Wiener-Hopf Factorization for Arithmetic Brownian Motion with Time-Dependent Drift and Volatility (with T. R. Bielecki and Z. Cheng). Stochastic Processes and Their Applications, 156, pp. 246 - 290, 2023.  DOI: 10.1016/j.spa.2022.11.002

• Estimation of Tempered Stable Lévy Models of Infinite Variation (with J. E. Figueroa-López and Y. Han). Methodology and Computing in Applied Probability, 24(2), 713 - 747, 2022. DOI: 10.1007/s11009-022-09940-7

• Wiener-Hopf Factorization Technique for Time-Inhomogeneous Markov Chains (with T. R. Bielecki, Z. Cheng, and I. Cialenco). Stochastics: An International Journal of Probability and Stochastic Processes, 93(1), 130 - 166, 2021. DOI: 10.1080/17442508.2019.1708913

• Wiener-Hopf Factorization for Time-Inhomogeneous Markov Chains and Its Application (with T. R. Bielecki, I. Cialenco, and Y. Huang). Probability and Mathematical Statistics, 40(2), 225 - 244, 2020. DOI: 10.37190/0208-4147.40.2.3

• Bayesian Estimations for Diagonalizable Bilinear SPDEs (with Z. Cheng and I. Cialenco). Stochastic Processes and Their Applications, 130(2), 845 - 877, 2020. DOI: 10.1016/j.spa.2019.03.020

• Stochastic Representations for Solutions to Nonlocal Bellman Equations (with C. Mou and A. Swiech). Annals of Applied Probability, 29(6), 3271 - 3310, 2019. DOI: 10.1214/19-AAP1473

• On the Fairness Performance of NOMA-Based Wireless Powered Communication Networks (with Y. Liu, X. Chen, L. X. Cai, Q. Chen, and D. Tang). Proceedings of IEEE International Conference on Communications, 2019. DOI: 10.1109/ICC.2019.8761702

• Performance Analysis of Energy Harvesting in Wireless Networks Using Stochastic Geometry (with Z. Chen, Z. Chen, L. X. Cai, and Y. Cheng). Proceedings of IEEE International Conference on Green Computing and Communications, pp. 280 – 286, 2018. DOI: 10.1109/Cybermatics_2018.2018.00076

• Trajectory Fitting Estimators for SPDEs Driven by Additive Noise (with I. Cialenco and Y. Huang). Statistical Inference for Stochastic Processes, 21(1), pp. 1 – 19, 2018. DOI: 10.1007/s11203-016-9152-2 

• Short-Time Expansions for Call Options on Leveraged ETFs under Exponential Lévy Models with Local Volatility (with J. E. Figueroa-López and M. Lorig). SIAM Journal on Financial Mathematics, 9(1), pp. 347 – 380, 2018. DOI: 10.1137/17M1111292 

• Lower Bounds on the Generalized Central Moments of Optimal Alignments Score of Random Sequences (with C. Houdré and J. Lember). Journal of Theoretical Probability, 31(2), pp. 643 – 683, 2018. DOI: 10.1007/s10959-016-0730-4 

• Third-Order Short-Time Expansions for Close-to-the-Money Option Prices Under the CGMY Model (with J. E. Figueroa-López and C. Houdré). Applied Mathematical Finance, 24(6), pp. 547 – 574, 2017. DOI: 10.1080/1350486X.2018.1429935 

• High-Order Short-Time Expansions for ATM Option Prices of Exponential Lévy Models (with J. E. Figueroa-López and C. Houdré). Mathematical Finance, 26(3), pp. 516 – 557, 2016. DOI: 10.1111/mafi.12064 . Note: This is an extension of our earlier version: High-order short-time expansions for ATM option prices under the CGMY model. arXiv:1112.3111 

• Small-Time Expansions of the Distributions, Densities, and Option Prices of Stochastic Volatility Models with Lévy Jumps (with J. E. Figueroa-López and C. Houdré).  Stochastic Processes and Their Applications, 122(4), pp. 1808 – 1839, 2012. DOI: 10.1016/j.spa.2012.01.013 

• A Viscosity Approach to a Stochastic Control Problem on a Bounded Domain (with C. Houdré). Preprint, 2019. arXiv:0911.0956

• A Central Limit Theorem for the Optimal Alignments Score in Multiple Random Words (with C. Houdré and U. Islak). Preprint, 2016. arXiv:1512.05699

• Feynman-Kac Formulae for Solutions to Degenerate Elliptic and Parabolic Boundary Value and Obstacle Problems with Partial Dirichlet Boundary Conditions. (with P. M.N. Feehan and J. Song). Preprint, 2015. arXiv:1509.03864 

Selective Talks 

• SIAM Conference on Financial Mathematics and Engineering, Contributed Lecture Session on Stochastic Control and Optimization Problems in Financial Mathematics, University of Toronto, Toronto, Ontario, Canada, June 4 – 7, 2019. (Stochastic Representations for Nonlocal Bellman Equations) 

• Washington University in St. Louis, Financial Mathematics Seminar, March 7, 2019. (Wiener-Hopf Factorization for Time-Inhomogeneous Markov Processes) 

• Georgia Institute of Technology, Stochastics Seminar, February 26, 2019. (Wiener-Hopf Factorization for Markov Processes) 

• University of Wisconsin – Milwaukee, Mathematical Science Colloquium, November 16, 2018. (Stochastic Representations for Nonlocal Bellman Equations) 

• Third Eastern Conference on Mathematical Finance. Illinois Institute of Technology, Chicago, IL, October 26 – 28, 2018. (Small-Time Asymptotic Methods in Financial Mathematics) 

• Illinois Institute of Technology, Mathematical Finance, Stochastic Analysis, and Machine Learning Seminar, October 16, 2018. (An Overview of Wiener-Hopf Factorization) 

• Illinois Institute of Technology. Mathematical Finance, Stochastic Analysis, and Machine Learning Seminar, September 25, 2018. (Stochastic Representations for Nonlocal Bellman Equations) 

• 2018 World Energy and Electricity Youth Scholar Forum, Intelligent Information and Control Subforum. North China Electric Power University, Beijing, China, May 18 – 20, 2018. (Small-Time Asymptotic Methods in Financial Mathematics) 

• Special Lecture on Financial Mathematics. North China Electric Power University, Baoding, China, May 17, 2018. (Small-Time Asymptotic Methods in Financial Mathematics) 

• Illinois Institute of Technology, Mathematical Finance and Stochastic Analysis Seminar, January 18, 2018. (Stochastic Representations for Nonlocal Bellman Equations) 

• INFORMS 19th Applied Probability Society Conference, Special Session on Financial Engineering. Northwestern University, Evanston, IL, July 10 – 12, 2017. (Small-Time Asymptotics for Options on Leveraged ETFs under Exponential Lévy Models with Local Volatility) 

• AMS Spring Central Sectional Meeting #1127, Special Session on Financial Mathematics and Statistics. Indiana University, Bloomington, IN, April 1 – 2, 2017. (Small-Time Asymptotics for Options on Leveraged ETFs under Exponential Lévy Models with Local Volatility) 

• Worcester Polytechnic Institute, Financial Mathematics and Stochastic Analysis Common, March 13, 2017. (Small-Time Asymptotics for Lévy-Based Models) 

• Illinois Institute of Technology, Applied Mathematics Colloquium. February 20, 2017. (Small-Time Asymptotics for Options on Leveraged ETFs under Exponential Lévy Models with Local Volatility) 

• INFORMS Annual Meeting, General Session on Probabilistic Combinatorial Optimization. Nashville, TN, November 13 – 16, 2016. (Limiting Theorems for the Optimal Alignments Score in Multiple Random Words) 

• Georgia Institute of Technology, Stochastic Seminar. October 27, 2016. (Small-Time Asymptotics for Options on Leveraged ETFs under Exponential Lévy Models with Local Volatility) 

• Purdue University, Computational Finance Seminar. March 30, 2016. (Small-Time Asymptotics for Lévy-Based Models) 

• Illinois Institute of Technology, Discrete Applied Mathematics Seminar. February 24, 2016. (Limiting Theorems for the Optimal Alignments Score in Multiple Random Words) 

• Joint Mathematics Meetings 2016, AMS Special Session on Problems and Challenges in Financial Engineering and Risk Management. Seattle, WA, January 6 – 9, 2016. (High-Order Short-Time Expansions of ATM Option Prices under Exponential Lévy Models) 

• Georgia Institute of Technology, Mathematical Finance and Financial Engineering Seminar. October 21, 2015. (Small-Time Asymptotics for Lévy-Based Models) 

• AMS Fall Central Sectional Meeting #1112, Special Session on Stochastic Analysis with Applications to Quantitative Finance. Loyola University Chicago, Chicago, IL, October 3 – 4, 2016. (Lower Bounds on the Generalized Moments of the Optimal Alignments Score of Random Sequences) 

• Beijing Normal University, Probability Seminar. July 9, 2015. (Small-Time Asymptotics for Lévy-Based Models) 

• Youth Probability Forum, Peking University. Beijing, P. R. China, July 6 – 8, 2015. (Feynman-Kac Formulas for Degenerate Elliptic Boundary Value Problems) 

• Conference on Mathematical Finance and Partial Differential Equations. Rutgers, The State University of New Jersey, New Brunswick, NJ, May 1, 2015. (Small-Time Asymptotics for Lévy-Based Models) 

Conference Organization 

• SIAM Conference on Financial Mathematics and Engineering 2021, Mini-Symposium on High-Frequency and Short-Term Driven Methods in Financial Mathematics (with J. E. Figueroa-López). Philadelphia, PA, June 1 – 4, 2021.

• AMS Special Session on Random Matrices, Random Percolation and Random Sequence Alignments (with M. Damron). Joint Mathematics Meetings 2017, Atlanta GA, January 4 – 7, 2017. 

• Mini-Symposium on Stochastic Control Theory With Applications to Finance (with G. Wang). SIAM Conference on Financial Mathematics & Engineering, Austin, TX, November 17 – 19, 2016. 

• Special Session on Stochastic Analysis with Applications to Quantitative Finance (with I. Cialenco). AMS Fall Central Sectional Meeting #1112, Loyola University Chicago, Chicago, IL, October 2 – 4, 2015. 

• Special Session on Partial Differential Equations, Stochastic Analysis, and Applications to Mathematical Finance (with P. M.N. Feehan and C. Pop). AMS Fall Eastern Section Meeting #1093, Temple University, Philadelphia, PA, October 12 – 13, 2013. 

• The Fifth and Sixth Graduate Student Probability Conference (with A. Hoffmeyer, H. Huynh, J. Ma, R. Wang, and L. Xin). Georgia Institute of Technology, Atlanta, GA, April 29 – May 1, 2011 & April 27 – 29, 2012. 

Useful Links 

• arXiv, MathSciNet 

• Chicago Symphony Orchestra 

• Golden State Warriors, FC Barcelona, Chicago Cubs