Dr. Arun Kumar

Associate Professor
  • Department of Mathematics
  • Indian Institute of Technology Ropar
  • Rupnagar, Punjab - 140001, India
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Dr. Arun Kumar received his PhD degree in Mathematics from IIT Bombay in 2012. He also holds a Master degree in Industrial Mathematics from IIT Roorkee. His PhD work is related to Subordinated Stochastic Processes that have applications in finance, fractional partial differential equations and statistical physics. During his stint in financial industry as a research analyst, he worked on all the major asset classes i.e. Fixed Income, Equity, Currency, and Commodity. Further, he possess a good experience in pricing and analysis of Bonds, Swaps, Total Return Swaps, Swap Curve Construction, Bonds Portfolio, Interest Rate Swaps Portfolio, Bond Futures, Cheapest to Deliver Calculations.
  • Ph.D from Indian Institute of Technology Bombay, India, 2012.
  • M.Sc in Mathematics, Indian Institute of Technology Roorkee, India, 2005.
  • Associate Professor, IIT Ropar – April 2022 – Till Present
  • Assistant Professor, IIT Ropar – Dec 2016 – March 2022
  • Visiting Scientist, Wroclaw University of Science and Technology, Poland — May 28 – July 2, 2017
  • Assistant Professor, IIM Sirmaur – Jul 2016 – Dec 2016
  • Visiting Scientist, ISI Chennai – Jan 2016 – June 2016
  • Visiting Assistant Professor, IIT Madras, Chennai – Jan 2015 – Dec 2015
  • Research Analyst, ARP Research LLP, Mumbai – Dec 2011 – Nov 2014
Journal Publications
40. Pande, N. K., Kumar, A. and Gupta, A.K. (2026). Robust Mean Field Game of Autonomous Vehicles on Multilane Roadways via Attention-based Adversarial Networks. To Appear in Proceedings of the Royal Society A.
39. Pande, N. K., Kumar, A. and Gupta, A.K. (2026). Physics integrated adaptive residual learning framework for traffic state estimation. Engineering Analysis with Boundary Elements. 188, 106751.
38. Priti, and Kumar, A. (2026). Space–time fractional diffusion with stochastic resetting. Statist. Probab. Lett. 227, 110528.
37. Rani, M. Garg, B. and Kumar, A. (2025). Application of the variance gamma distribution for change point detection. To Appear in Communications in Statistics – Simulation and Computation.
36. Rani, M., Garg, B. and Kumar, A. (2025). Change point analysis in data with heavy tails: a Normal Inverse Gaussian approach. Economics Letters, 254, 112477.
35. Pande, N.K., Pasricha, P., Kumar, A. and Gupta, A. K. (2025). European Option Pricing in Regime Switching Framework via Physics-Informed Residual Learning. Expert Systems with Applications, 128226.
34. Pande, N. K., Kumar, A. and Gupta, A.K. (2025). Forecasting Stock Indices: Stochastic and Artificial Neural Network Models. Computational Economics, 65, 1937 – 1969.
33. Pande, N. K., Jain, A., Kumar, A. and Gupta, A. K. (2024). Conservative Deep Neural Networks for Modeling Competition of Ribosomes with Extended Length. Physica D: Nonlinear Phenomena, 470, 134415.
32. Dhull. M.S., Kumar, A. and Wylomanska, A. (2024). The expectation-maximization algorithm for autoregressive models with normal inverse Gaussian innovations. Commun. Stat. B: Simul. Comput. 53 (11), 5421-5441.
31. Dhull, M.S. amnd Kumar, A. (2024). Geometric infinitely divisible autoregressive models. Statistical Papers, 65, 4515-4536.
30. Gupta, N., Kumar, A., Leonenko, N. N. and Vaz, J. (2024). Generalized fractional derivatives generated by Dickman subordinator and related stochastic processes. Fractional Calculus and Applied Analysis, 27, 1527–1563.
29. Bhootna, N. and Kumar, A. (2024). Tempered stable autoregressive models. Communications in Statistics-Theory and Methods, 53(2), 765-785.
28. Bhootna, N. and Kumar, A. (2024). GARTFIMA process and its spectral density based estimation. Journal of Applied Statistics, 51 (10), 1919-1945.
27. Gupta, N. and Kumar, A. (2023). Fractional Poisson processes of order k and beyond. Journal of Theoretical Probability, 36(4), 2165-2191.
26. Bhootna, N., Dhull, M.S., Kumar, A. and Leonenko, N. (2023). Singularities of spectral densities of Humbert generalized fractional differencing processes. Communications in Non-linear Science and Numerical Simulations, 125, 107412.
25. Dhull, M. S. and Kumar, A. (2022). Expectation-Maximization Algorithm for Autoregressive Models with Cauchy Innovations . Engineering Proceedings, 18, 21.
24. Jain, A., Kumar, A. and Gupta, A. K. (2022). A theoretical framework to analyse the flow of particles in a dynamical system with stochastic transition rates and site capacities. Royal Society Open Science 9 (10), 220698.
23. Kumar, A. and Gupta, N. (2022). Inverse tempered stable subordinators and related processes with Mellin transform. Statist. Probab. Lett. 186, 109465.
22. Gupta, N., Kumar, A. and Leonenko, N. (2022). A generalization of multifractional Brownian motion. Fractal and Fractional, 6, 74-85.
21. Grzesiek, A., Poloczanski, R., Kumar, A. and Wylomanska, A. (2021). Moment-based estiamtion of parameters of general inverse subordinator, Physica A, 126042.
20. Dhull. M.S. and Kumar, A. (2021). Normal inverse Gaussian autoregressive model using EM algorithm, IntJ. Adv. Eng. Sci. Appl. Math. 13, 139-147.
19. Gupta, N., Kumar, A., and Leonenko, N. (2021). Stochastic Models With Mixtures of Tempered Stable Subordinators. Mathematical Communications, 26, 77-99.
18. Gupta, N., Kumar, A., and Leonenko, N. (2020). Skellam Type Processes of Order k, Entropy, 1193-1213.
17. Gupta, N., Kumar, A., and Leonenko, N. (2020). Tempered Fractional Poisson Processes and Fractional Equations With Z-Transform. Stochastic Analysis and Applicaitons. 38, 939-957.
16. Kumar, A., Leonenko, N. and Pichler, A. (2020). Fractional Risk Process in Insurance. Mathematics and Financial Economics, 14, 43 - 65.
15. Gajda, J., Wylomanska, A. and Kumar, A. (2019). Fractional Levy stable motion time-changed by gamma subordinator. Communications in Statistics – Theory and Methods. 48, 5953-5968.
14. Gajda, J., Kumar, A. and Wylomanska, A. (2019). Stable Levy Process Delayed by Tempered Stable Subordinator. Statist. Probab. Lett. 145, 284–292.
13. Kumar, A., Maheshwari, A. and Wyłomańska, A. (2019). Linnik Lévy process and some extensions. Physica A, 529, 121539.
12. Kumar, A., Wylomanska, A., Gajda, J. and Poloczanski, R. (2019). Fractional Brownian motion delayed by tempered and inverse tempered stable subordinators. Methodol. Comput. Appl. Probab., 21, 185-202.
11. Kumar, A., Upadhye, N., Wylomanska, A., Gajda, J. (2019). Tempered Mittag-Leffler Levy Processes. Communications in Statistics, 48(2), 396-411.
10. Kumar, A. and Nane, E. (2018). On Infinite Divisibility of the Distribution of Some Inverse Subordinators. Modern Stochastics: Theory and Applications, 5(4), 509-519.
9. Vellaisamy, P. and Kumar, A. (2018). First-Exit Times of an Inverse Gaussian Process, Stochastics, 1, 29-48.
8. Kumar, A., Wylomanska, A. and Gajda, J. (2017). Stable Levy motion with inverse Gaussian subordinator. Physica A, 482, 486-500.
7. Gazda, J., Wylomanska, A. and Kumar, A. (2017). Generalized fractional Laplace motion. Statist. Probab. Lett., 124, 101-109.
6. Kumar, A., Wyomanska, A. and Poloczanski, R. and S. Sundar (2017). Fractional Brownian motion time-changed by gamma and inverse gamma process. Physica A, 468, 648667.
5. Wylomanska, A., Kumar, A., Poloczanski, R. and Vellaisamy, P. (2016). Inverse Gaussian and its inverse process as the subordinators of fractional Brownian motion. Physical Review E 94 (4), 042128.
4. Kumar, A. and Vellaisamy, P. (2014). Inverse Tempered Stable Subordinators. Statist. Probab. Lett. 103, 134-141.
3. Kumar, A. and Vellaisamy, P. (2012). Fractional normal inverse Gaussian process. Methodology and Computing in Applied Probability. 14, 263-283.
2. Kumar, A., Nane, E. and Vellaisamy, P. (2011). Time-Changed Poisson Processes. Statist. Probab. Lett. 81, 1899-1910.
1. Kumar, A., Meerschaert, M. M. and Vellaisamy, P. (2011). Fractional normal inverse Gaussian diffusion. Statist. Probab. Lett. 81, 146-152.
  1. “Introductory Statistics for Social Scientists” at Panjab University on Mar 30, 2022.
  2. Two Sessions on “Stochastic Calculus I and Stochastic Calculus II” at Panjab University on January 05, 2022.
  3. Two sessions on “Introduction to Data Science and Introductory Statistics” at NIELIT on September 23-24, 2021.
  4. Two sessions on “Machine Learning and Optimization Techniques: Applications to Financial Markets” at IIT Mandi, July 12-13 on 2021.
  5. “Expectation Maximisation Algorithm” at IIT Ropar organised by Indo-Taiwan Joint Research Centre on AI and ML held on January 30, 2021.
  6. Took couple of sessions in “Two Week Workshop on Scientific Computing Using Matlab and Python” organised by Department of Mathematics J C Bose University during September 07-18, 2020.
  7. “Statistical Techniques in Research and Data Analysis” at IIT Ropar as part of Research Methodology Series on May 23, 2020.
  8. “Subordinated Stochastic Processes and Anomalous Diffusion” at IIT Ropar as part of APJ Lecture Series on March 4, 2020.
  9. “Introduction to Python” at Panjab University Chandigarh during Jan 8-9, 2020, where an FDP was organized on MATHEMATICAL COMPUTATIONAL SKILLS: A PRACTICAL APPROACH”
  10. A five days workshop on “Statistical Techniques for AI and Data Science” at IIT Ropar during Dec 9-13, 2019.
  11. “Clustering Techniques in Statistical Learning” at IIM Indore on September 24, 2019.
  12. “Subordinated Stochastic Processes and Continuous Time Random Walks” at IIIT Delhi on March 14, 2019.
  13. “Probability & Statistics With Applications” at DAVIET Jalandhar on February 15, 2019.
  14. “Introduction to Data Science” at Indian Institute of Management Indore, on Jan 23, 2019.
  15. “Option Pricing Under Multi-Period Binomial Model” at Indian Institute of Management Indore, on Jan 22, 2019.
  16. “Introduction to Data Science Using Python” at Lyallpur Khalsa College Jalandhar on December 23, 2018.
  17. “Option Pricing Under Multi-Period Binomial Model” at Indian Institute of Management Indore, on Jan 25, 2018.
  18. “Subordinated Stochastic Processes” at Wroclaw University of Science and Technology, Poland on Jun 7, 2017.
  19. “Mathematical Finance: Theory and Practice” at IIT Madras from Jan 16-21, 2017.
  20. “R Application to Quantitative Finance” at BITS Goa from Aug 26-28, 2016.
  21. “Applications of Probability and Statistics for Engineers” at Easwari Engineering College, Chennai on Apr 1, 2016.
  22. “Applications of Probability and Statistics for Engineers” at VIT Chennai on Mar 16, 2016.
  23. “Applications of Probability and Statistics” at VIT Chennai on Feb 1, 2016.
  24. Short-term course for AICTE approved engineering colleges’ teachers on “Classical and Bayesian Statistics” at IIT Madras during Sep 22 – Sep 26, 2015.
  25. “Subordinated Stochastic Processes” at ISI Delhi on Jul 30, 2014.
  26. “Bond, Valuation, Risk, Returns and Beyond” at ICT Mumbai on Nov 3, 2012.
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