{ probability + statistics + finance + analysis + stochastic control }
As (an applied) mathematician, I find fascinating the process of solving new real-life and impactful problems by applying, and usually developing, rigorous mathematical methods and techniques. At general level, my research focuses on understanding the random phenomena in various stochastic models, and stays at intersection of probability, statistics, finance, real analysis and stochastic control, with emphasis on financial markets, risk management and applications of Stochastic PDEs.
Mathematical Finance: Dynamic performance and dynamic risk measures, Nonlinear market models, Counterparty risk and CCPs, Model Risk.
Statistics: Statistical Inference for Stochastic PDEs and Stochastic ODEs
Probability and Stochastic Processes: Wiener-Hopf factorization for Markov chains, Stochastic PDEs, Stochastic control
Functional Analysis: Spectral analysis of nonselfadjoint operator.
See also: My Google Scholar Profile, ORCID, List of publications (with links to pdfs), My PhD students and postdocs, and past research talks
Support Acknowledgement
My research has been supported through grants:
NSF Grant DMS - 1907568/1907522 "Collaborative Research: Risk-Averse Control of Markov Systems with Model Uncertainty", 2019-2023, co-Pis with Tomasz R. Bielecki (Illinois Tech) and Andrzej Ruszczynski (Rutgers University).
NSF Grant DMS-1211256, “Topics in stochastic processes and mathematical finance: counterparty risk valuation and hedging, Markov consistency and Markov copulae, and dynamic performance assessment indices”, (Co-Pi with T.R. Bielecki), 2012-2015;
NSF Grant DMS-0938234, "NSF/CBMS Regional Conference in the Mathematical Sciences Recent Advances in the Numerical Approximation of Stochastic Partial Differential Equations" (Co-PI with F. Hickernell and J. Duan), 2010;
NSF Grant DMS-0908099, "AMC-SS: Mathematical foundations of responsible risk management in credit markets", (Co-Pi with T.R. Bielecki), 2009-2012.
Service to Scientific Community
Chair (2022-2023) and Program Director (2020-2021) for SIAM Activity Group on Financial Mathematics and Engineering
Managing Editor for International Journal of Theoretical and Applied Finance (IJTAF), World Scientific
Associate Editor
Applied Mathematical Finance (Taylor & Francis)
International Journal of Financial Engineering (JFE), World Scientific
Statistical Inference for Stochastic Processes (SISP), Springer
Member of the steering committee for the Eastern Conference of Mathematical Finance series
Reviewer for (30+ journals):
Acta Mathematica Applicatae Sinica (English Series), Advances in Difference Equations, Applied Mathematics – A Journal of Chinese Universities, Annals of Applied Probability (AAP), Applied Mathematics Letters, Communications on Pure and Applied Analysis, Finance and Stochastics, Indian Journal of Pure and Applied Mathematics, International Journal of Theoretical and Applied Finance (IJTAF), Journal of Applied Mathematics and Physics (ZAMP), Journal of Mathematical Analysis and Applications, Journal of Statistical Planning and Inference, Journal of Theoretical Probability, Latin American Journal of Probability and Mathematical Statistics, Management Science, Mathematical Finance, Mathematics of Operations Research (MOR), Methodology and Computing in Applied Probability, Probability, Uncertainty and Quantitative Risk (PUQR), Modern Stochastics: Theory and Applications, Quantitative Finance, Statistical Inference for Stochastic Processes (SISP), Statistics and Probability Letters, Stochastics and Dynamics, Stochastic Processes and their Applications (SPA), SIAM Journal on Control and Optimization, SIAM Journal on Financial Mathematics, SIAM Journal for Multiscale Modeling and Simulation, SIAM Journal on Numerical Analysis, MathSciNet Mathematical Reviews of American Mathematical SocietyCurrent research projects and areas of expertise
Stochastic Control under Model Uncertainty
Risk Filtering and Risk-Averse Control of Markovian Systems Subject to Model Uncertainty (with Tomasz R. Bielecki and Andrzej Ruszczyński), submitted for publication (27 pages), 2022. arXiv PDF
Risk-sensitive Markov decision problems under model uncertainty: finite time horizon case (with Tomasz R. Bielecki, and Tao Chen), In: Yin, G., Zariphopoulou, T. (eds) Stochastic Analysis, Filtering, and Stochastic Optimization. Springer, Cham, pp. 33-52, 2022. DOI: 10.1007/978-3-030-98519-6_2 . arXiv PDF
Acceptability Maximization (with Gabriela Kováĉova and Birgit Rudloff), Frontiers of Mathematical Finance, June 1(2), pp.219-248, 2022. DOI: 10.3934/fmf.2021009 arXiv PDF
Time-inconsistent Markovian control problems under model uncertainty with application to the mean-variance portfolio selection (with Tomasz R. Bielecki, and Tao Chen), International Journal of Theoretical and Applied Finance, 24(1) 2150003 (28 pages), 2021. DOI: 10.1142/S0219024921500035 arXiv PDF
Adaptive Robust Control Under Model Uncertainty (with Tomasz R. Bielecki, Tao Chen, Areski Cousin and Monique Jeanblanc) Forthcoming in SIAM Journal on Control and Optimization (SICON) (22 pages), 2017.
Recursive Construction of Confidence Regions (with Tomasz R. Bielecki and Tao Chen) Electronic Journal of Statistics, 11(2), pp. 4674-4700, 2017. DOI:10.1214/17-EJS1362
Statistical Inference for SPDEs
For recent developments in the area of Statistics for SPDEs visit Stats4SPDEs - a web site that aims to serve as an informational platform for the scientific community interested in this topic.
Relevant Publications
Anisotropic Viscosities estimation for the stochastic Primitive equations (with Ruimeng Hu and Quyuan Lin), Preprint (33 pages), 2023. arXiv PDF
Statistical analysis of discretely sampled semilinear SPDEs: a power variation approach (with Hyun-Jung Kim and Gregor Pasemann), submitted for publication (21 pages), 2021. ararxiv.org/abs/2103.04211Xiv, PDF
Parameter estimation for semilinear SPDEs from local measurements (Randolf Altmeyer and Gregor Pasemann), submitted for publication (46 pages), 2020, arXiv, PDF
Parameter estimation for discretely sampled stochastic heat equation driven by space-only noise revised (with Hyun-Jung Kim), Stochastic Processes and their Applications, 22, pp. 1-30, 2022. DOI: 10.1016/j.spa.2021.09.012 arXiv PDF
Drift estimation for discretely sampled SPDEs (with Francisco Delgado-Vences, and Hyun-Jung Kim) Stoch PDE: Anal Comp, 8, pp. 895–920, 2020. DOI: 10.1007/s40072-019-00164-4 arXiv PDF
Statistical Analysis of Some Evolution Equations Driven by Space-Only Noise (with Hyun-Jung Kim, and Sergey Lototsky) Statistical Inference for Stochastic Processes, 23, 83–103, 2020. DOI: 10.1007/s11203-019-09205-0 arXiv PDF
Bayesian Estimations for Diagonalizable Bilinear SPDEs (with Ziteng Cheng and Ruoting Gong) Stochastic Processes and their Applications, 20(2), pp. 845-877, 2020 (preprint 2018) DOI:10.1016/j.spa.2019.03.020 arXiv, PDF
Statistical Inference for SPDEs: an overview, Statistical Inference for Stochastic Processes, 21(2), pp 309-329, 2018. DOI:10.1007/s11203-018-9177-9, arXiv, PDF
A note on parameter estimation for discretely sampled SPDEs (with Yicong Huang) Stochastics and Dynamics 20(3), pp. 2050016, 2020 (28 pages, preprint 2017). DOI:10.1142/S02194937205001, arXiv, PDF
Trajectory Fitting Estimators for SPDEs Driven by Additive Noise (with Ruoting Gong and Yicong Huang) Statistical Inference for Stochastic Processes, 21(1), pp. 1-19, 2018 (accepted for publication 2016).DOI:10.1007/s11203-016-9152-2, arXiv, PDF
A note on error estimation for hypothesis testing problems for some linear SPDEs (with Liaosha Xu) Stochastic Partial Differential Equations: Analysis and Computations, September 2014, vol. 2, No 3, pp. 408-431.DOI:10.1142/S0219024913500027, arXiv
Hypothesis testing for stochastic PDEs driven by additive noise (with Liaosha Xu) Stoch Proc and App, 125(3), March 2015, pp. 819-866, DOI:10.1016/j.spa.2014.09.022, arXiv, PDF
Parameter estimation for stochastically perturbed Navier-Stokes Equations (with Nathan Glatt-Holtz) Stochastic Processes and their Applications, vol 121, pp. 701-724, 2011. DOI:10.1016/j.spa.2010.12.007, arXiv
Parameter estimations for SPDEs with multiplicative fractional noise, Stochastics and Dynamics, Vol. 10, No. 4, pp 561-576, 2010, DOI: 10.1142/S0219493710003091 arXiv
Asymptotic Properties of the Maximum Likelihood Estimator for Stochastic Parabolic Equations with Additive Fractional Brownian Motion (with Sergey V. Lototsky and Jan Pospisil) Stochastics and Dynamics, Vol. 9, No. 2, pp. 169-185, 2009 DOI: 10.1142/S0219493709002610 arXiv
Parameter estimation in diagonalizable bilinear stochastic parabolic equations (with Sergey V. Lototsky) Statistical Inference for Stochastic Processes, vol 12, No.3, pp. 203-219, 2009 DOI: 10.1007/s11203-008-9031-6 arXiv
Risk Management
Time consistency of dynamic risk measures and dynamic performance measures generated by distortion functions (with Tomasz R. Bielecki and Hao Liu), Preprint (25 pages), 2023. PDF ; with Supplement to "Time consistency of dynamic risk measures and dynamic performance measures generated by distortion functions" (with Tomasz R. Bielecki and Hao Liu), 26 pages, 2023. PDF
Risk Filtering and Risk-Averse Control of Markovian Systems Subject to Model Uncertainty (with Tomasz R. Bielecki and Andrzej Ruszczyński), forthcoming in Math Meth Oper Res (27 pages), 2022. arXiv PDF
Risk-sensitive Markov decision problems under model uncertainty: finite time horizon case (with Tomasz R. Bielecki, and Tao Chen), In: Yin, G., Zariphopoulou, T. (eds) Stochastic Analysis, Filtering, and Stochastic Optimization. Springer, Cham, pp. 33-52, 2022. DOI: 10.1007/978-3-030-98519-6_2 . arXiv PDF
Acceptability Maximization (with Gabriela Kováĉova and Birgit Rudloff), Frontiers of Mathematical Finance, June 1(2), pp.219-248, 2022. DOI: 10.3934/fmf.2021009 arXiv PDF
Estimation of Fair Capital Risk Allocation (with Tomasz R. Bielecki, Marcin Pitera and Thorsten Schmidt), forthcoming in Statistics & Risk Modeling (24 pages), 2019. arXiv, PDF
A Dynamic Model of Central Counterparty Risk (with Tomasz R. Bielecki, and Shibi Feng) International Journal of Theoretical and Applied Finance, Vol. 21, No. 08, 1850050 (32 pages), 2018. DOI:10.1142/S0219024918500504. Featured article, and editor's choice on IJTAF (free access for registered users).
A survey of time consistency of dynamic risk measures and dynamic performance measures in discrete time: LM-measure perspective (with Tomasz R. Bielecki and Marcin Pitera) Probability, Uncertainty and Quantitative Risk, 2:3, pp.1-52, 2017. DOI:10.1186/s41546-017-0012-9
Dynamic Conic Finance via Backward Stochastic Difference Equations (with Tomasz R. Bielecki and Tao Chen) SIAM Journal of Financial Mathematics, 6(1), 1068-1122. (55 pages), 2015. DOI:10.1137/141002013
A unified approach to time consistency of dynamic risk measures and dynamic performance measures in discrete time (with Tomasz R. Bielecki and Marcin Pitera) Mathematics of Operations Research, 43(1), pp. 204-221, 2018.DOI:10.1287/moor.2017.0858
Dynamic Limit Growth Indices in Discrete Time (with Tomasz R. Bielecki and Marcin Pitera) Stochastic Models, vol. 31, pp. 494-523, 2015 (preprint 2013). DOI:10.1080/15326349.2015.1053616
Dynamic Assessment Indices (with Tomasz R. Bielecki, Samuel Drapeau and Martin Karliczek) Stochastics: An International Journal of Probability and Stochastic Processes, vol. 88, No 1, pp. 1-44, 2016 (accepted March 2015, preprint 2013) DOI:10.1080/17442508.2015.1026346
Dynamic Conic Finance: Pricing and Hedging in Market Models with Transaction Costs via Dynamic Coherent Acceptability Indices (with Tomasz R. Bielecki, Ismail Iyigunler and Rodrigo Rodriguez) Int. J Theoretical and App Finance, vol. 16, No 1, 2013. DOI:10.1142/S0219024913500027
Dynamic Coherent Acceptability Indices and their Applications to Finance (with Tomasz R. Bielecki and Zhao Zhang) Mathematical Finance, Volume 24, Issue 3, pp. 411-441, July 2014 (accepted Nov 2011) DOI:10.1111/j.1467-9965.2012.00524.x
Nonlinear Pricing Models
Arbitrage-Free Pricing of Derivatives in Nonlinear Market Models (with Tomasz R. Bielecki and Marek Rutkowski) Probability, Uncertainty and Quantitative Risk 3:2, 2018 (56 pages). DOI:10.1007/10.1186/s41546-018-0027-x
Dynamic Conic Finance via Backward Stochastic Difference Equations (with Tomasz R. Bielecki and Tao Chen) SIAM Journal of Financial Mathematics, 6(1), 1068-1122. (55 pages), 2015. DOI:10.1137/141002013
No-Arbitrage Pricing for Dividend-Paying Securities in Discrete-Time Markets with Transaction Costs (with Tomasz R. Bielecki, and Rodrigo Rodriguez) Forthcoming in Mathematical Finance, 2012. DOI:10.1111/mafi.12038
Dynamic Conic Finance: Pricing and Hedging in Market Models with Transaction Costs via Dynamic Coherent Acceptability Indices (with Tomasz R. Bielecki, Ismail Iyigunler and Rodrigo Rodriguez) International Journal of Theoretical and Applied Finance, vol. 16, No 1, 2013. DOI:10.1142/S0219024913500027
Stochastic Analysis
Wiener-Hopf factorization for time-inhomogeneous Markov chains (with Tomasz R. Bielecki, Ziteng Cheng and Ruoting Gong) Forthcoming in Stochastics: An International Journal Of Probability And Stochastic Processes, 2019.
Wiener-Hopf factorization for time-inhomogeneous Markov chains and its application (with Tomasz R. Bielecki, Ruoting Gong and Yicong Huang) forthcoming in Probability and Mathematical Statistics (19 pages), 2018.
Approximation of Stochastic Partial Differential Equations by a Kernel-based Collocation Method, (with Gregory E. Fasshauer and Qi Ye) International Journal of Computer Mathematics, vol. 89, No 18, pp.2543-2561, 2012.DOI:10.1080/00207160.2012.688111