### { 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

Part of **my current research is supported** by the National Science Foundation **(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).

**Past support through grants:** **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

**Program Director** 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)**:**

## Current 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**

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

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

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