I have successfully supervised six Ph.D. student, and have two
further Ph.D. students under my supervision. My past students, the
titles of their theses are the date of their graduations are
respectively:
- Conall Kelly: On the Oscillatory Behaviour of Stochastic Delay Equations , graduated November 2005.
- Siobhan Devin: On the asymptotic behaviour of deterministic and stochastic Volterra integro-differential equations,
graduated November 2007, funded by IRCSET Embark Initiative
- Catherine Swords: Stochastic Delay Difference and Differential Equations: Applications to Financial Markets, Graduated November 2009
- Huizhong Wu: Pathwise Large Deviations of Stochastic Differential Equations with Applications to Finance, Graduated November 2009, funded by SFI Research Frontiers Programme.
- Terry Lynch: Large Fluctuations of Stochastic Differential Equations: Regime Switching and Applications to Simulation and Finance,
Graduated November 2010, funded by IRCSET Embark Initiative
- Michael McCarthy: Explosions and Unbounded Growth in
Nonlinear Delay Differential Equations: Numerical and Asymptotic Analysis, graduated November 2011, funded by IRCSET Embark Initiative
The theses of Swords, Wu and Lynch have been published as research
monographs by Lambert Academic Publishers:
- Catherine Swords, Stochastic Delay Difference and Differential Equations: Applications to Financial Markets, 180pp,
LAP Lambert Academic Publishing, 2010, ISBN-13: 978-3838334752.
- Huizhong Wu, Pathwise Large Deviations of Stochastic Differential Equations with Applications to Finance,
200 pages, LAP LAMBERT Academic Publishing, 2010, ISBN-13:
978-3838360447.
- Terry Lynch, Large Fluctuations of Stochastic Differential Equations: Regime Switching and Applications to Simulation and Finance, 240 pages, LAP LAMBERT Academic Publishing, 2010, ISBN-13: 978-3843359351.
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Currently, I have two further PhD students. The provisional titles
of their theses, the starting date and expected graduation dates, as
well as the agency funding their research, are recorded below:
- Jian Cheng: Asymptotic Behaviour of Stable Nonlinear Differential Equations and their Discretisations when Perturbed by Noise,
started October 2008, due to graduate November 2012, funded by SFI Mathematics Initiative.
- John Daniels: Volatility modelling in inefficient markets, started October 2008, due to graduate November 2012, funded by IRCSET Embark Initiative and SFI Mathematics Initiative.
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In the last ten years, I have supervised the dissertations of 25
students on the taught MSc programme in Financial and Industrial
Mathematics. The names of the students and titles of the projects
are as follows: As can be gleaned from the project titles, most of
the projects are in the field of stochastic differential equations
or financial mathematics.
- Jonathon Byrne, CreditMetrics and Credit Risk, 1999
- Brendan Needham, Herd Behaviour in Financial Markets, 1999
- Damian Jenkinson, Noise Trader risk in Financial Markets, 2000
- Anthony Carroll, Linear Stochastic Delay-differential equations, 2000
- Aoife Flynn, Stabilisation and Destabilisation of Functional Differential Equations by Noise, 2001
- Jacques Prevost, Stability of stochastic delay equations with small delay, 2002
- Alan Burke, Stochastic Volatility, 2002
- Peter Durkan, Stochastic and deterministic models of competition, 2003
- Rachel McCarthy, Non-exponential stability of dynamical systems, 2003
- Elayne Kelly, Delay models of commodity price fluctuation, 2003
- Brendan Cullen. Explosions in solutions of stochastic functional equations, 2004
- David Martin. Highly correlated Guassian processes, 2004
- Brian Gilligan. Non-exponential asymptotic behaviour of stochastic differential equations, 2004
- Sebastien Brunetti The optimal consumption problem, 2004
- John Driver. Fixed point theory and financial markets with memory, 2006
- Therese Fallon. Large fluctuations of solutions of stochastic differential equations, with applications to heavy tailed asset returns, 2006
- Derbhla O'Grady. Market bubbles and finite time explosion of stochastic differential equations, 2006
- Carl Williams. Investor sentiment models, 2006
- Stephen Tapley. Models of noise trading in financial markets, 2006
- Jian Cheng. Asymptotic Behaviour of Stochastic Functional Differential Equations with Maximum Functionals, 2007
- Alessio Calcagno. Stability of Stochastic differential Equations with Fading Stochastic Perturbations, 2007
- Triona Forde. Numerical Analysis of Nonlinear Stochastic Differential Equations and Applications to Option Pricing, 2008
- Laura DiSalvo. Preservation and Destruction of Limit Cycles under stochastic perturbations, 2009
- Aidan Monahan. Asymptotic behaviour of a continuous--time market model with an average functional, 2010
- Scott McDonald. Simulation in a discrete--time market model with an average functional, 2010
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If anyone is interested in pursuing doctoral research, please e-mail me, and I will be glad to discuss forthcoming projects with you. A good source of funding for prospective postgraduate students, especially those who are currently undergraduates in
Ireland, is The Embark Initiative, supported by IRCSET (the Irish Research Council for Science Engineering and Technology). Anyone interested in pursuing PhD research starting in the 2012/2013 academic year should contact me before 31 January 2012 at the latest, as the call closes on 15 February 2012.
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john.appleby{at}dcu.ie
http://webpages.dcu.ie/~applebyj/PhD