Dr. Arun Kumar

Assistant Professor

arun.kumar [AT] iitrpr.ac.in


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 at ARP Research LLP, Mumbai, as a research analyst, he worked on all the major asset classes i.e. Fixed Income, Equity, Currency, and Commodity. Further, he possess a very 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 etc.

Areas of Research

Probability Theory and Stochastic Processes


Ph.D from Indian Institute of Technology Bombay, India, 2012.
M.Sc in Mathematics, Indian Institute of Technology Roorkee, India, 2005.

Work Experience

Assistant Professor, IIT Ropar – Dec 2016 - Till Present
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

Selected Publications/Patents

16. Kumar, A., Leonenko, N. and Pichler, A. (2019). Fractional Risk Process in Insurance. Mathematics and Financial Economics (To Appear)
15. Gajda, J., Wylomanska, A. and Kumar, A. (2019). Fractional Levy stable motion time-changed by gamma subordinator. Communications in Statistics (Forthcoming).
14. Kumar, A., Maheshwari, A. and Wyłomańska, A. (2019).  Linnik Lévy process and some extensions. Physica A, 529, 121539.
13. Gajda, J., Kumar, A. and Wylomanska, A. (2019). Stable Levy Process Delayed by Tempered Stable Subordinator. Statist. Probab. Lett. 145, 284-292.
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: Theory and Methods. 48, 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, 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, 648–667.
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

Other Information

Invited Talks


  1. "Clustering Techniques in Statistical Learning" at IIM Indore on September 24, 2019.
  2. "Subordinated Stochastic Processes and Continuous Time Random Walks" at IIIT Delhi on March 14, 2019.
  3. "Probability & Statistics With Applications" at DAVIET Jalandhar on February 15, 2019.
  4. "Introduction to Data Science" at Indian Institute of Management Indore, on Jan 23, 2019.
  5. "Option Pricing Under Multi-Period Binomial Model" at Indian Institute of Management Indore, on Jan 22, 2019.
  6. "Introduction to Data Science Using Python" at Lyallpur Khalsa College Jalandhar on December 23, 2018.
  7. "Option Pricing Under Multi-Period Binomial Model" at Indian Institute of Management Indore, on Jan 25, 2018.
  8. "Subordinated Stochastic Processes" at Wroclaw University of Science and Technology, Poland on Jun 7, 2017.
  9. “Mathematical Finance: Theory and Practice” at IIT Madras from Jan 16-21, 2017.
  10. “R Application to Quantitative Finance” at BITS Goa from Aug 26-28, 2016.
  11. “Applications of Probability and Statistics for Engineers” at Easwari Engineering College, Chennai on Apr 1, 2016.
  12. “Applications of Probability and Statistics for Engineers” at VIT Chennai on Mar 16, 2016.
  13. “Applications of Probability and Statistics” at VIT Chennai on Feb 1, 2016.
  14. Short-term course for AICTE approved engineering colleges’ teachers on “Classical and Bayesian Statistics” at IIT Madras during Sep 22 - Sep 26, 2015.
  15. “Subordinated Stochastic Processes” at ISI Delhi on Jul 30, 2014.
  16. “Bond, Valuation, Risk, Returns and Beyond” at ICT Mumbai on Nov 3, 2012.