Dr Timothy Johnson

Department of Actuarial Mathematics and Statistics
and the Maxwell Institute for Mathematical Sciences,
Heriot-Watt University,
Edinburgh, EH14 4AS,
United Kingdom

E-mail: T.C.Johnson( at )

I am a lecturer (associate professor) in the Department of Actuarial Mathematics and Statistics. My current research focus is investigating financial networks using agent based models and techniques of complex network theory. Specifically, I am interested in the effect that different commercial cultures have on the resilience and effectiveness of the financial networks they give rise to. Any potential PhD students interested in modelling financial systems as complex networks can contact me. My background is in the field of optimal decision making under uncertainty, where my research focused on optimal stochastic control. I am currently working on developing a methodology to assess different power storage technologies based on stochastic control techniques.

I completed my PhD in Applied Probability at King's College London in November 2006, supervised by Prof. Mihail Zervos. The thesis was The Optimal Timing of Investment Decisions. I have a BSc in physics from Imperial College and worked in the energy industry for 16 years, initially on reservoir simulation but more recently addressing problems of valuation and asset management. I obtained my MSc in Financial Mathematics from King's College in 2002, my dissertation was on Modelling Commodity Futures Prices with a Multi-Factor State Model. 

I joined Heriot-Watt in September 2006 as the UK Research Council's Academic Fellow in Financial Mathematics. As an academic fellow I had a responsibility to explain the science of financial mathematics to the general public. From June to December 2009 I also held an Edinburgh Beltane Beacon for Public Engagement Fellowship with the objective of developing events to better engage the public with the scientific aspects of finance. An outcome of these activies has beeen an interest in the relationship between ethics, mathematics and finance, resulting in my paper Reciprocity as a foundation of Financial Mathematics. I blog on the relationship between finance, science and democracy at  Magic, Maths and Money.

I was co-organiser on the workshop Mathematics in the Management of Energy Systems, held on 29th January 2008, a direct descendent of this meeting was the Energy Systems Week held at the Isaac Newton Centre in 2010. I organised the Financial Mathematics theme at Maths2010, the joint British Mathematics Colloquim / British Applied Mathematics Colloquim Meeting of 2010. This coincided with the Edinburgh International Science Festival and as part of the Festival and as a result of my Beltane Fellowship I organised and participated in a panel discussion involving Prof Donald Mackenzie, Dr Gillian Tett and, Ms Terri Duhon.  I organised the first IMA conference on Mathematics in Finance in 2013 and am deputy chair of the organisisng comittee for the second IMA conference.

I am Programme Director for the MSc in Quantitative Financial Engineering (QFE).

Publications and Working Papers

1.      T. C. Johnson and M. Zervos, The solution to a second order linear ordinary differential equation with a non-homogeneous term that is a measure., Stochastics , Vol 79, Issue 3&4, pgs 363-382, (2007). DOI: 10.1080/17442500601100281

2.      A. J. Jack, T. C. Johnson and M. Zervos, A singular control problem with application to the Goodwill Problem. Stochastic Processes and their Applications, Volume 118, Issue 11, Pages 2098-2124, (2008) . DOI: 10.1016/

3.      T. C. Johnson and M. Zervos, The explicit solution to a sequential switching problem with non-smooth data., Stochastics: an International Journal of Probability and Stochastic Processes 82:1 (2010), 69-109. DOI: 10.1080/17442500903106606

4.      D. Eager, J. Bialek and T. Johnson, Validation of a dynamic control model to simulate investment cycles in electricity generating capacity, Power and Energy Society General Meeting, (2010) IEEE, DOI: 10.1109/PES.2010.5589365.

5.      T. C. Johnson, What is Financial Mathematics., in The Best Writing on Mathematics:2010, Edited by Mircea Pitic, (2011) Princeton University Press.

6.      F. Alazemi, T. C. Johnson, and M. Zervos Buy-low Sell-high investment strategies. Mathematical Finance, 23:3 (2013), 560-578. DOI: 10.1111/j.1467-9965.2011.00508.x

7.      T. C. Johnson, Book Review Donald Mackenzie, An Engine, Not a Camera: How Financial Models Shape Market. Annals of Actuarial Science, Vol. 5, part 2, pp. 297-298. DOI: 10.1017/S1748499511000157

8.      T. C. Johnson, Reciprocity as a foundation of Financial Mathematics, Journal of Business Ethics, 131:1 (2015), pages 43-67. DOI: 10.1007/s10551-014-2257-x (open access).

9.      T. C. Johnson, The solution of some discretionary stopping problems. In press, IMA Journal of Mathematical Control and Information. DOI:10.1093/imamci/DNV060

10.      T. C. Johnson, Mathematics and Finance: Where is the ethical malaise? The Mathematical Intelligencer, 37:4 (2015) pages 8-11. DOI:10.1007/s00283-015-9573-6

11.      L. El-Ghandour ,T. C. Johnson, A methodology to assess the economic impact of power storage technologies., Phil. Trans. A .

[Actuarial Mathematics & Statistics] [Maxwell Institute for Mathematical Sciences] [School of Mathematical and Computer Sciences] [Heriot-Watt University]