Duy Nguyen - Research

Referee for several journals including: AMS Mathematics Reviews, Automatica, Australian & New Zealand Journal of Statistics, Applied mathematics finance, Decisions in Finance and Economics, SIAM Journal on Control and Optimization, SIAM journal on Financial Mathematics, SIAM Conference on Control and Applications, IEEE conference on Decision and Control Theory, Mathematics of Operations Research, European Journal of Operation Research, Journal of Economic Dynamics and Control, Insurance: Mathematics and Economics, INFORMS Journal on Computing, Journal of Optimization Theory and Applications, Operations Research Letters, International Journal of Theoretical and Applied Finance, Finance Research Letters, Nonlinear Analysis: Hybrid Systems, IET Control Theory & Applications, Journal of Forecasting, Physica A: Statistical Mechanics and its Applications, Computer & Mathematics with Applications, Stochastic Models, Applied Mathematics and Computations, Numerical Mathematics: Theory, Methods and Applications, Communications in Statistics: Theory and Methods, North American Journal of Economics and Finance, Advances in Difference Equations, etc.

A) Preprints/working papers

49. On short-time behavior of implied volatilities in a market with indexes (joint with H. Chau and T. Nguyen)

48. Continuous time optimal investment consumption: A reinforcement learning approach (joint with H. Chau and T. Nguyen)

47. Approximate hedging with transaction cost under regime switching models (joint with H. Chau and T. Nguyen)

B) Published/Accepted

46. Natural gradient variational Bayes without Fisher matrix analytic calculations and its inversion (joint with A.Godichon-Baggioni, and M-N. Tran)
Journal of the American Statistical Association, forthcoming

45. Moments of Student’s t-distribution: A unified approach (joint with J. Kirkby and D.H. Nguyen)

Modern Stochastics: Theory and Applications, forthcoming

44. An efficient method to simulate diffusion bridges (joint with H. Chau, J. Kirkby, D.H. Nguyen , N. Nguyen and T. Nguyen)
Statistics and Computing, forthcoming

43. Pymle: A python package for maximum likelihood estimation and simulation of stochastic differential equations (joint with, J. Kirkby, D.H. Nguyen, and N. Nguyen)
Journal of Statistical Software, forthcoming

42. On the inversion-free Newton’s method and its applications (joint with H. Chau, J. Kirkby, D.H. Nguyen , N. Nguyen and T. Nguyen)

International Statistical Review, forthcoming.

41. Essential Aspects of Bayesian data imputation (joint with William Holt)
Springer Foundations for Undergraduate Research in Mathematics books series, forthcoming.

40. Stability and stabilization of coupled jump diffusions and applications (joint with D.H.Nguyen, N. Nguyen, and G. Yin)

Journal of Differential Equations, 379(15), 175-206, 2024

39. Spline local basis methods for nonparametric density estimation (joint with J. Kirkby and A. Leitao)

Statistics Surveys, 17, 75-118 (2023)

38. Inversion-free subsampling Newton's method for large sample logistic regression (joint with J. Kirkby and D.H.Nguyen and N. Nguyen)

Statistical Papers, 63, 943-963 (2022).

37. Maximum likelihood estimation of diffusion using continuous time Markov chain (joint with J. Kirkby and D.H.Nguyen and N. Nguyen)

Computational Statistics and Data Analysis, Volume 168, April 2022, 107408.

36. Variational Bayes on Manifolds (joint with D.H.Nguyen and M-N. Tran)

Statistics and Computing, 2021 31(6), 1-17

35. Equity-linked guaranteed minimum death benefits with dollar cost averaging (joint with J. Kirkby)

Insurance: Mathematics and Economics, Volume 100, September 2021, Pages 408 - 428.

34. Nonparametric density estimation and bandwidth selection with B-spline bases: A novel Galerkin method (joint with J. Kirkby and A. Leitao)

Computational Statistics and Data Analysis, Volume 159, July 2021, 107202 .

33. Stability in distribution of path-dependent hybrid diffusion (joint with D.H.Nguyen and S.L. Nguyen)

SIAM Journal on Control and Optimization, 2021, 59 (1), 434 - 463.

32. Efficient simulation of generalized SABR and stochastic local volatility models based on Markov chain approximation (joint with Z. Cui and J. Kirkby)

European Journal of Operational Research, Volume 290, Issue 3, 1 may 2021, Page 1046 - 1062.

31. A closed form model free implied volatility formula through delta sequences (joint with Z. Cui , J. Kirkby and S. Taylor)

Journal of Derivatives, Summer 2021, 28 (4) 111 - 127.

30. A unified data-driven framework for consistent financial valuation and risk measurement (joint with Z. Cui and J. Kirkby)

European Journal of Operational Research, Volume 289, Issue 1, 16 February 2021, Pages 381 - 398.

29. A general continuous time Markov chain approximation for multi-asset option pricing with systems of correlated diffusions (joint with J. Kirkby and D.H.Nguyen)

Applied Mathematics and Computation, Volume 386, 1 December 2020, 125472.

28. An Analysis of Dollar Cost Averaging and Market Timing Investment Strategies (joint with J. Kirkby and S. Mitra)

European Journal of Operational Research, Volume 286, Issue 3, 1 November 2020, pages 1168 - 1186.

27. Efficient Asian option pricing under regime switching jump diffusions and stochastic volatility models (joint with J. Kirkby)

Annals of Finance, 16, 307-351 (2020) .

26. A Probabilistic approach to the moments of binomial random variables and application

The American Statistician, Volume 75, 2021 - Issue 1.

25. Nonparametric density estimation by B-spline duality (joint with Z. Cui and J. Kirkby)

Econometric Theory, 2020, 36(2), 250-291.

24. Full-fledged SABR through Markov chain (joint with Z. Cui and J. Kirkby)

Wilmott Journal, Volume 2019, Issue 102, page 74 - 81.

23. Continuous time Markov chain and regime switching approximations with applications to options pricing (joint with Z. Cui and J. Kirkby)

Modeling, Stochastic Control, Optimization, and Applications. The IMA volumes in Mathematics and Applications, Vol 164, July 2019, page 115-146.

22. A general framework for time-changed Markov processes and applications (joint with Z. Cui and J. Kirkby)

European Journal of Operational Research, 2019, 273(2), 785-800.

21. A hybrid Markov chain-tree valuation framework for stochastic volatility jump diffusion models.

International Journal of Financial Engineering, Vol.5, No. 4 (2018), 1850039 (30 pages).

20. A General Valuation Framework for SABR and Stochastic Local Volatility Models (joint with Z. Cui and J. Kirkby)

SIAM Journal on Financial mathematics, 2018, 9(2), 520-563.

19. An integral presentation for elasticity and sensitivity for stochastic volatility models (joint with Z. Cui and H. Park )

Mathematics and Financial Economics, March 2018, Vol 12, Issue 2, pp. 249-274.

18. Integral representation of probability density of stochastic volatility models and timer options (joint with Z. Cui , J. Kirkby, and G. Lian)

International Journal of Theoretical and Applied Finance, Vol 20, No. 08, 1750055 (2017).

17. A general framework for discretely sampled realized volatility derivatives in stochastic volatility models with jumps (joint with Z. Cui and J. Kirkby)

European Journal of Operational Research -Volume 262, Issue 1, 1 October 2017, Pages 381-400

16. A unified approach to American and barrier options under stochastic volatility models with jumps (joint with Z. Cui and J. Kirkby)

Journal of Economic Dynamics and Control- Volume 80, July 2017, Pages 75-100

15. Equity-linked annuity pricing with cliquet-style guarantees in regime switching and stochastic volatility models with jumps (joint with Z. Cui and J. Kirkby)

Insurance: Mathematics and Economics - Volume 74, May 2017, Pages 46-62

14. First hitting time of integral function of diffusions and applications (joint with Z. Cui).

Stochastic Models - Volume 33, 2017, Issue 3, Pages 1-16.

13. Magnitude and speed of consecutive market crashes in a diffusion model (joint with Z. Cui).

Methodology and Computing in Applied Probability, Accepted

12. A unified tree approach for options pricing under stochastic volatility models (joint with C.C. Lo and K. Skindilias).

Finance Research Letters, Volume 20, February 2017, Pages 260-268

11. Omega diffusion risk model with surplus-dependent tax and capital injection, (joint with Z. Cui).

Insurance: Mathematics and Economics, Volume 68, May 2016, Pages 150–161.

10. A recombining tree method for option pricing with state-dependent switching rates (joint with J. Jiang and R.H. Liu)

International Journal of Theoretical and Applied Finance - Vol. 19, No. 2 (2016) 1650012 (26 pages).

9. Density of Generalized Verhulst Process and Bessel Process with Constant Drift (joint with Z. Cui).

Lithuanian Mathematical Journal, Volume 56, No. 4, 2016, pp. 463-473.

8. Numerical schemes for pricing Asian options under state-dependent regime switching jump diffusion models, (joint with D.M. Dang and G. Sewell)

Computers & Mathematics with Applications -Volume 71, Issue 1, January 2016, Pages 443–458

7. A tree approach to options pricing under regime switching jump diffusion models, (joint with R.H. Liu)

International Journal of Computer Mathematics-(Special issue on computational methods in Finance)-Volume 92, Issue 12, 2015

6. Pairs trading: An optimal selling rule, (joint with K.Kuo, P.Luu, E.Perkerson, K. Thompson, and Q.Zhang)

Mathematical Control and Related Fields-Volume 5, Number 3, September 2015

5. An optimal trading rule under a switchable mean reversion model, (joint with J. Tie and Q. Zhang).

Journal of Optimization Theory and Applications, April 2014, Vol.161, Issue 1,145-163

4. A stochastic approximation approach for trend-following trading, (joint with G. Yin and Q. Zhang)

Hidden Markov Models in Finance- International Series in Operations Research & Management Science Vol. 209 (2014), 167-184

3. Stock trading rule under a switchable market, (joint with J. Tie and Q. Zhang).

Mathematical Control and Related Fields, 209-231, Vol.3, Issue 2, 2013

2. First cohomology for finite groups of Lie type: simple modules with small dominant weights, (joint with the UGA VIGRE Algebra Group)

Transactions of The American Mathematics Society, 365, (2013), No. 2, 1025-1050

1. Trend-following trading using recursive stochastic optimization algorithms, (joint with G. Yin and Q. Zhang)

Proceeding of 52nd IEEE Conference on Decision and Control, 7827-7832, Florence, Italy, December, 2013

C) Notes

Here are some notes I wrote:

Options pricing in a binomial model with transaction costs.

Derivative note

D) Reviewed articles for

- Mathematical Reviews

- Finance Research Letters

- SIAM Conference on Control and Its Applications (CT17)

- Operations Research Letters

- Journal of Control theory and Technology

- IET Control Theory & Applications

- SIAM Journal on Control and Optimization

- European Journal of Operation Research

- Computers & Mathematics with Applications

- Journal of Optimization Theory and Applications

- International Journal of Computer Mathematics

- International Journal of Theoretical and Applied Finance

- Journal of Systems Science & Complexity

- Journal of Applied mathematics and computation

- Journal of Forecasting

- The World 52nd conference in decision and control theory

E) Talks given

- A general valuation framework for SABR and stochastic local volatility models, PDEs and Mathematical Finance seminar, Rutgers University, May 17-19th, 2017.

- A general valuation framework for SABR and stochastic local volatility models, Invited talk, 2017 SIAM conference in stochastic control and its applications: Applications of stochastic system in finance and energy, July 9-July 12, 2017.

- First hitting time of integral functional of diffusions and applications, Invited talk, Mathematical finance seminar, Worcester Polytechnic Institute, November 2015

-Optimal asset trading under regime switching model, Invited talk, Applied maths seminar, University of Massachusetts - Lowell, September 30, 2015

- A recombining tree method for options pricing in regime switching jump diffusion models, Invited talk, PDEs and Mathematical Finance seminar, Rutgers University, September 1st, 2015

-Poster: A finite horizon optimal consumption and portfolio selection problem in a regime switching jump diffusion model, Carnegie Mellon University, 06- 2015

-Numerical schemes for pricing Asian options under state-dependent regime switching jump diffusion models, Maths Fin. and PDE, Rutgers Univ, May 2015.

-Stochastic approximation approach for trend following, Invited talk, AMS Spring Eastern sectional meeting, U of Maryland, Baltimore, March 2014

-Stochastic approximation approach for trend following, Mathematics Colloquium, Williams College, March 2014

-A new combined tree method for option pricing under mixed Gaussian diffusion models, Mathematics Colloquium, MCLA March 2014

-Stochastic approximation approach for trend following, Invited talk, Ho Chi Minh University of Science, Vietnam, December 2013

-Stochastic approximation approach for trend following, Invited talk, Hoa Sen University, Vietnam December 2013.

- Optimal trading under regime switching models, Mathematics Colloquium, MCLA October 2013

- Optimal asset trading under regime switching models - Thesis defense , University of Georgia , July 2013

- An optimal trading rule under switchable mean-reversion model, VIGRE seminar, University of Georgia, October 2012

- An optimal trading rule under switchable market, The 5th European summer school in mathematical finance, Ecóle Polytechnique, Paris, August 2012 (cancelled)

- An optimal trading rule under switchable market, SIAM conference in financial maths, U of Minnesota July 11 2012

- An optimal trading rule under switchable mean-reversion model , Mock AMS student conference UGA, June 2012

- An optimal trading rule under switchable market, Applied and computation maths seminar - Ohio University -May 17, 2012

- From binomial model to Black-Scholes formula: A discrete approach, VIGRE graduate student seminar, UGA, Oct, 4th, 2011

- Modifying the mean-variance approach to avoid violations of stochastic dominance, Financial presentation, UGA, Sept 22nd, 2011

- From binomial model to Black-Scholes formula, Financial presentation, UGA, Sept, 2011

- An optimal trading rule under switchable mean-reversion model, Oral exam, UGA, Sept, 13rd, 2011

- An optimal trading rule under switchable mean-reversion model, Applied maths seminar, UGA, Sept, 7th, 2011

- On the Riemann-Rock theorem and Euler characteristics of toric varieties, Toric variety presentation, UGA, May 2010

- Ito integral, Moc AMS conference, UGA, July 2010

- C-normality in finite groups, ICE-EM Australian graduate school in mathematics, The University of Queensland, Australia, July 2006

- 2015 Fifth International IMS-FIPS Workshop , Rutgers University, June 2015

- Conference on Methods of Mathematical Finance , Carnegie Mellon University, June 2015.

- Conference on stochastic analysis and related fields, Purdue University, USA, May, 2015.

- Mathematics Finance and Partial Differential Equations, Rutgers Univ, May 2015.

-Stochastic Partial Differential Equation summer school, MSRI, University of California at Berkeley, July 2014.

- AMS Spring Eastern sectional meeting, U of Maryland, Baltimore, March 2014

F) Conferences and workshops attended

- The 5th European summer school in financial mathematics, Ecóle Polytechnique, Paris, August 2012

- July 7-8,2012 SIAM financial maths conference at University of Minnesota - Twines city

- April 27/2017 Graduate student probability conference at Georgia Institute of Technology

- Feb 25/2012 Georgia Scientific computing symposium at University of Georgia

- 05/2010: VIGRE 2010 Summer School Program, The University of Georgia, Athens, GA –U.S.A

- 06/2008 : International conference in Algebra and its application, Ohio University, Athens, Ohio- U.S.A

- 05/2007 : The XXIXth Ohio State-Denison Mathematics Conference May 16th -18th 2008, The Ohio State University, Columbus, Ohio, U.S.A

- 07/2006 : ICE-EM gradschool in mathematics at The University of Queensland, Brisbane, Australia ,

G) Research Experience

I am interested in Mathematical finance but I also enjoy my time being a member of the following research groups:

- Fall 2012 and Spring 2013, The VIGRE mathematics finance research group led by professor Q. Zhang

- Fall 2011 and Spring 2012, The VIGRE low-rank matrix approximation research group led by professor M.J. Lai

- Fall 2010 and Spring 2011, The VIGRE dynamical arithmetic research group led by professor R. Rumely

- Spring 2010, The VIGRE Algebra research group led by professor B. Boe working on cohomology of finite groups

- Fall 2009 , The VIGRE Algebra research group led by professor D. Nakano working on cohomology of finite groups