## Research

**Research Area:** Financial Mathematics

**Research Profile:** *Financial mathematics*

Tom Hurd laid the foundation for financial mathematics at McMaster when he initiated Phimac activities in 1998. He is currently Director of the MFM program (MPhimac). After an extensive research career in mathematical physics, he turned to the mathematical study of financial markets in the late 1990s. Since then he has built an international research reputation, with many publications in areas such as portfolio theory, interest rate modeling, and credit risk. His work is currently focussed on modeling systemic risk, that is, the stability of financial networks, and he has recently published a book on the subject. Over the years, he has supervised numerous M.Sc. and Ph.D. research students in financial mathematics, many of whom have moved on to careers in banking.

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## Publications

Books

- Contagion! Systemic Risk in Financial Networks. T. R. Hurd. Springer Briefs in Financial Mathematics, 2016.
- QED: A Proof of Renormalizability. J. Feldman, T.R. Hurd, L. Rosen, J. Wright. Springer. 1987.

Published Research Papers

- T. R. Hurd, "Bank Panics and Fire Sales, Insolvency and Illiquidity", to appear in International Journal of Theoretical and Applied Finance (IJTAF), arxiv.org/abs/1711.05289, 2018.
- Eduardo Santos Diaz, Simon Haykin, T.R. Hurd, "The Fifth-Degree Continuous-Discrete Cubature Kalman Filter for Radar", IET Radar, Sonar & Navigation. 10.1049/iet-rsn.2018.5148, 2018.
- P. Jevtic and T. R. Hurd. “The joint mortality of couples in continuous time”, Insurance Mathematics and Economics, 75, 90-97, 2017.
- T. R. Hurd, James Gleeson, Sergey Melnik,
*"A framework for analyzing contagion in banking networks"*, PLOS ONE, 12, 1-20, 2017, DOI 10.1371/journal.pone.0170579.
- T. R. Hurd, Davide Cellai, Sergey Melnik, Quentin Shao, "Double Cascade Model of Financial Crises", International Journal of Theoretical and Applied Finance (IJTAF), 19:5, 1-27, 2016. Download pdf file
- T. R. Hurd, "The Construction and Properties of Assortative Configuration Graphs", in "Recent Progress and Modern Challenges in Applied Mathematics, Modeling and Computational Science", Fields Institute Communications, ed. Roderick Melnik, Springer-Verlag Berlin, 2016. Download pdf file
- Yacine Aït-Sahalia, T. R. Hurd, Portfolio Choice in Markets with Contagion", Journal of Financial Econometrics, 14, 1-28, 2015. Download pdf file
- T. R. Hurd, James Gleeson
*"On Watts' Cascade Model with Random Link Weights", *Journal of Complex Networks, 1, 25-43, 2013. Download pdf file
- James Gleeson, T. R. Hurd, Sergey Melnik, Adam Hackett
*"Systemic risk in banking networks without Monte Carlo simulation"*, to appear in "Advances in Network Analysis and its Applications", Mathematics in Industry series, ed. E. Kranakis, Springer Verlag, Berlin Heidelberg New York, 2011. Download pdf file
- M. Grasselli, T. R. Hurd
*“The Fields Institute Thematic Program on Quantitative Finance: Foundations and Applications January to June, 2010”* Quantitative Finance, 11, 21 - 29, 2011. Download pdf file
- Chuang Yi, A. Tchernitser, T. R. Hurd
*"Randomized structural models of credit spreads"*, Quantitative Finance, 2010, http://www.informaworld.com/10.1080/14697688.2010.507213. DOI: 10.1080/14697688.2010.507213

Download pdf file
- Ienkaran Arasaratnam, Simon Haykin, T. R. Hurd
*"Cubature Filtering for Continuous-Discrete Systems: Theory with an Application to Tracking"*, IEEE Transactions on Signal Processing, 2010, 29 pages.

Download pdf file
- T. R. Hurd, Zhuowei Zhou
*"A Fourier transform method for spread option pricing”*, SIAM Journal of Financial Mathematics, **1**, 142-157, 2009. Download pdf file
- T. R. Hurd
*“Credit Risk Modelling using time-changed Brownian motion”*, Int. J. Theor. App. Fin. **12**, 1213–1230, 2009. Download pdf file
- T. R. Hurd, A. Kuznetsov
*"On the first passage time for Brownian motion subordinated by a Levy process"*, Journal of Applied Probability **46.1**, 181-198, 2009. Download pdf file
- T. R. Hurd
*"Saddlepoint approximations in portfolio credit risk"*, in Encyclopedia of Quantitative Finance, ed. R. Cont, Wiley-UK, 7 pages, 2008. Download pdf file
- Y. Ait-Sahalia, J. Cacho-Diaz, T. Hurd
*"Portfolio Choice with Jumps: A Closed Form Solution" *, Annals of Applied Probability,**19.2**, 277-290, 2008. Download pdf file
- T. R. Hurd, A. Kuznetsov
*"Explicit formulas for Laplace transforms of stochastic integrals"*, Markov Processes and Related Fields, **14**, 277-290, 2008. Download pdf file
- T. R. Hurd, A. Kuznetsov
*"Affine Markov chain models of multifirm credit migration"*, Journal of Credit Risk **3**, 3-29, 2007. Download pdf file
- M. R. Grasselli, T. R. Hurd
*"Indifference pricing and hedging for volatility derivatives"*, Applied Mathematical Finance **14**, 303-317, 2007. Download pdf file
- Jingping Yang, T. R. Hurd, Xuping Zhang
*"Saddlepoint approximation method for pricing CDOs"*, Journal of Computational Finance **10**, 1-20, 2006. Download pdf file
- T. R. Hurd
*"A note on log-optimal portfolios in exponential Levy markets"*, Statistics and Decisions, **22**, pp. 225-236, 2004. Download pdf file
- M. R. Grasselli, T. R. Hurd
*"Weiner chaos and the Cox-Ingersoll-Ross model"*, Proc. R. Soc. A, **461**, pp. 459-479, 2004. Download pdf file
- T. Choulli, T. R. Hurd
*"The role of Hellinger processes in mathematical finance"*, Entropy **3**, pp. 152-163, 2001. Download pdf file
- J. Boland, T.R. Hurd, M. Pivato, L. Seco
*"Measures of dependence for multivariate Levy distributions"*, Proceedings of the Conference on Disordered and Complex Systems, edited by P. Sollich et al, American Institute of Physics, 2001. Download ps file ; pdf file

## Graduate Students

Currently Supervising:

John Heisey (MSc, CSE)

Hassan Chehaitli (PhD, CSE)