## Biography

I am Interested in the design and analysis of computational techniques for the solution of stochastic differential equations. Such equations are used to model real-world systems subject to noisy feedback or uncertainty, for example in financial markets, neuroscience, or ecology.This kind of research blends coding and theoretical mathematics, and if you are interested in pursuing a PhD or Masters in it you can contact me by email and I'll be happy to discuss it.

From January 2022 to December 2023 I am part of the Royal Society of Edinburgh Saltire Research Facilitation Network on Stochastic Differential Equations: Theory, Numerics, and Applications.

Currently serving as Director of the MSc Financial and Computational Mathematics at UCC, and as an executive member of the committee of the Irish Mathematical Society.

How I got here: after finishing a PhD at Dublin City University in 2005 I spent a year at UCC as a postdoc in the SFI funded Probability Group. In 2006 I moved to the Mona campus of the University of the West Indies (UWI) in Kingston, Jamaica, where I spent eleven years. After completing a term as Head of the Department of Mathematics at UWI I returned to Ireland to UCC in 2017.

Google Scholar profile.

Publications indexed on MathSciNet.

Reviews published on MathSciNet.

Preprints on arXiv since 2016.

## Research Interests

Stochastic difference and differential equations;Numerical methods for stochastic differential equations;

Applications including in finance.

## Research Grants

Project | Funding Body | Start Date | End Date | Award | |
---|---|---|---|---|---|

SEFS New Connections Award | 25-JUL-22 | €2,289.41 | |||

Indonesia Endowment Fund for Education: Stochastic Models for Employee Stock Options | Other: Not Listed | 02-OCT-17 | 30-SEP-21 | €125,140.00 | |

College of SEFS Start-up fund. | Miscellaneous | 01-SEP-17 | 31-AUG-20 | €2,500.00 | |

American Institute for Mathematics: Stochastic stabilisation of limit-cycle dynamics in ecology and neuroscience | Other: Not Listed | 10-FEB-14 | 27-MAY-16 | €20,230.17 | |

London Mathematical Society Scheme 2 grant | Other: Not Listed | 02-JUN-14 | 13-JUN-14 | €1,605.96 | |

Johannes Kepler Universität Linz: Research Fellowship | Other: Not Listed | 11-MAY-14 | 31-MAY-14 | €2,292.20 | |

International Centre for Mathematical Sciences: Interaction of drift and noise structures in systems of stochastic ordinary differential equations arising from the spatial discretisation of stochastic partial differential equations: implications for numerical methods. | Other: Not Listed | 16-MAY-11 | 24-JUN-11 | €2,807.75 | |

UNESCO Mathematics Intervention Grant | Other: Not Listed | 01-SEP-09 | 31-AUG-10 | €6,986.17 | |

UWI Research and Publications Grant | Other: Not Listed | 24-MAY-10 | 28-MAY-10 | €692.25 | |

UWI New Initiative Grant: Linear Stability Methods for Systems of Stochastic Differential Equations | Other: Not Listed | 01-SEP-09 | 31-AUG-10 | €11,702.43 | |

London Mathematical Society Scheme 2 grant | Other: Not Listed | 12-JAN-09 | 23-JAN-09 | €1,228.63 | |

UWI Research and Publications Grant | Other: Not Listed | 03-MAR-08 | 07-MAR-08 | €450.75 | |

Enterprise Ireland Research Scholarship | Enterprise Ireland | 03-SEP-01 | 31-AUG-04 | €7,620.00 |

## Publications

### Peer Reviewed Journals

Year | Publication | |
---|---|---|

(2022) | 'Adaptive Euler methods for stochastic systems with non-globally Lipschitz coefficients' Cónall Kelly and Gabriel J. Lord (2022) 'Adaptive Euler methods for stochastic systems with non-globally Lipschitz coefficients'. Numerical Algorithms, 89 :721-747 [Details] | |

(2022) | 'The role of adaptivity in a numerical method for the Cox-Ingersoll-Ross model' Cónall Kelly, Gabriel Lord, and Heru Maulana (2022) 'The role of adaptivity in a numerical method for the Cox-Ingersoll-Ross model'. Journal of Computational and Applied Mathematics, 410 [DOI] [Details] | |

(2020) | 'Stabilization of cycles with stochastic prediction-based and target-oriented control' Braverman, E.; Kelly, Conall; Rodkina, A. (2020) 'Stabilization of cycles with stochastic prediction-based and target-oriented control'. Chaos, 30 :1-15 [DOI] [Full Text] [Details] | |

(2018) | 'Adaptive timestepping for pathwise stability and positivity of strongly discretised nonlinear stochastic differential equations' Cónall Kelly, Eeva Maria Rapoo, and Alexandra Rodkina (2018) 'Adaptive timestepping for pathwise stability and positivity of strongly discretised nonlinear stochastic differential equations'. Journal of Computational and Applied Mathematics, 334 (15):39-57 [Details] | |

(2018) | 'Adaptive timestepping for nonlinear stochastic systems' Cónall Kelly and Gabriel Lord (2018) 'Adaptive timestepping for nonlinear stochastic systems'. IMA Journal of Numerical Analysis, 38 (3):1523-1549 [DOI] [Details] | |

(2016) | 'Stabilisation of difference equations with noisy prediction based control' Elena Braverman, Cónall Kelly, and Alexandra Rodkina (2016) 'Stabilisation of difference equations with noisy prediction based control'. Physica D-Nonlinear Phenomena, 326 :21-31 [Details] | |

(2016) | 'Stochastic stability analysis of a reduced galactic dynamo model with perturbed α-effect' Cónall Kelly (2016) 'Stochastic stability analysis of a reduced galactic dynamo model with perturbed α-effect'. Physica A-Statistical Mechanics and Its Applications, 457 :480-491 [Details] | |

(2014) | 'Asymptotic and transient mean-square properties of stochastic systems arising in ecology, fluid dynamics and system control' Evelyn Buckwar and Cónall Kelly (2014) 'Asymptotic and transient mean-square properties of stochastic systems arising in ecology, fluid dynamics and system control'. Siam Journal On Applied Mathematics, 72 (2):411-433 [Details] | |

(2013) | 'Almost sure instability of the equilibrium solution of a Milstein-type stochastic difference equation' Cónall Kelly, Peter Palmer, and Alexandra Rodkina (2013) 'Almost sure instability of the equilibrium solution of a Milstein-type stochastic difference equation'. Computers & Mathematics with Applications, 66 (11):2220-2230 [Details] | |

(2013) | 'Corrigendum On the use of a discrete form of the Itˆo formula in the article “Almost sure asymptotic stability analysis of the θ-Maruyama method applied to a test system with stabilising and destabilising perturbations”' Gregory Berkolaiko, Evelyn Buckwar, Cónall Kelly, and Alexandra Rodkina (2013) 'Corrigendum On the use of a discrete form of the Itˆo formula in the article “Almost sure asymptotic stability analysis of the θ-Maruyama method applied to a test system with stabilising and destabilising perturbations”'. LMS Journal of Computation and Mathematics, 16 :366-372 [Details] | |

(2012) | 'Non-normal drift structures and linear stability analysis of numerical methods for systems of stochastic differential equations' Evelyn Buckwar and Cónall Kelly (2012) 'Non-normal drift structures and linear stability analysis of numerical methods for systems of stochastic differential equations'. Computers & Mathematics with Applications, 64 (7):2282-2293 [Details] | |

(2012) | 'Almost sure asymptotic stability analysis of the θ-Maruyama method applied to a test system with stabilising and destabilising perturbations' Gregory Berkolaiko, Evelyn Buckwar, Cónall Kelly, and Alexandra Rodkina (2012) 'Almost sure asymptotic stability analysis of the θ-Maruyama method applied to a test system with stabilising and destabilising perturbations'. LMS Journal of Computation and Mathematics, 15 :71-83 [Details] | |

(2011) | 'Sharp pathwise asymptotic stability conditions for planar systems of linear stochastic difference equations' Gregori Berkolaiko, Cónall Kelly, and Alexandra Rodkina (2011) 'Sharp pathwise asymptotic stability conditions for planar systems of linear stochastic difference equations'. Discrete And Continuous Dynamical Systems-Series S, :163-148 [Details] | |

(2010) | 'Towards a systematic linear stability analysis of numerical methods for systems of stochastic differential equations' Evelyn Buckwar and Cónall Kelly (2010) 'Towards a systematic linear stability analysis of numerical methods for systems of stochastic differential equations'. Siam Journal On Numerical Analysis, 48 (1):298-321 [Details] | |

(2010) | 'On the local dynamics of polynomial difference equations with fading stochastic perturbations' John A. D. Appleby, Cónall Kelly, Xuerong Mao, and Alexandra Rodkina (2010) 'On the local dynamics of polynomial difference equations with fading stochastic perturbations'. Dynamics of Continuous Discrete and Impulsive Systems: Series A - Mathematical Analysis, 17 :401-430 [Details] | |

(2010) | 'On the use of adaptive meshes to counter overshoot in solutions of discretised nonlinear stochastic differential equations' John A.D. Appleby, Cónall Kelly, and Alexandra Rodkina (2010) 'On the use of adaptive meshes to counter overshoot in solutions of discretised nonlinear stochastic differential equations'. International Journal of Difference Equations, 5 (2):129-148 [Details] | |

(2010) | 'Preserving positivity in solutions of discretised stochastic differential equations' John A.D. Appleby, Malgorzata Guzowska, Cónall Kelly, and Alexandra Rodkina (2010) 'Preserving positivity in solutions of discretised stochastic differential equations'. Applied Mathematics and Computation, 217 (2):763-774 [Details] | |

(2009) | 'Constrained Stability and Instability of Polynomial Difference Equations with State-Dependent Noise' Cónall Kelly and Alexandra Rodkina (2009) 'Constrained Stability and Instability of Polynomial Difference Equations with State-Dependent Noise'. Discrete and Continuous Dynamical Systems- Series A, 11 (4):1-21 [Details] | |

(2009) | 'Positivity and Stabilization for Nonlinear Stochastic Delay Differential Equations' John A. D. Appleby, Cónall Kelly, Xuerong Mao, and Alexandra Rodkina (2009) 'Positivity and Stabilization for Nonlinear Stochastic Delay Differential Equations'. Stochastics: An International Journal of Probability and Stochastic Processes, 81 (1):29-54 [Details] | |

(2008) | 'A Monte-Carlo approach to the effect of noise on local stability in polynomial difference equations' Cónall Kelly and Kirk Morgan (2008) 'A Monte-Carlo approach to the effect of noise on local stability in polynomial difference equations'. Matemáticas: Enseñanza Universitaria, 16 (2):3-10 [Details] | |

(2007) | 'Spurious oscillation in a uniform Euler discretisation of linear stochastic differential equations with vanishing delay' Appleby, JAD;Kelly, C (2007) 'Spurious oscillation in a uniform Euler discretisation of linear stochastic differential equations with vanishing delay'. Journal of Computational and Applied Mathematics, 205 :923-935 [DOI] [Details] | |

(2006) | 'Oscillation In A Nonuniform Discretisation of Linear Stochastic Differential Equations With Vanishing Delay' Appleby, JAD, Kelly, C; (2006) 'Oscillation In A Nonuniform Discretisation of Linear Stochastic Differential Equations With Vanishing Delay'. Dynamics of Continuous Discrete and Impulsive Systems: Series A - Mathematical Analysis, 13 (NA):535-550 [Details] | |

(2006) | 'Prevention of Explosions in Solutions of Functional Differential Equations by Noise Perturbation' John A. D. Appleby and Cónall Kelly (2006) 'Prevention of Explosions in Solutions of Functional Differential Equations by Noise Perturbation'. Dynamic Systems and Applications, 15 (2):227-240 [Details] | |

(2004) | 'Asymptotic and Oscillatory Properties of Linear Stochastic Delay Differential Equations with Vanishing Delay' John A. D. Appleby and Cónall Kelly (2004) 'Asymptotic and Oscillatory Properties of Linear Stochastic Delay Differential Equations with Vanishing Delay'. Functional Differential Equations, 11 (3-4):235-265 [Details] | |

(2004) | 'Oscillation and Non-oscillation in Solutions of Nonlinear Stochastic Delay Differential Equations' John Appleby and Conall Kelly (2004) 'Oscillation and Non-oscillation in Solutions of Nonlinear Stochastic Delay Differential Equations'. Electronic Communications In Probability, 9 :106-118 [Details] |

### Book Chapters

Year | Publication | |
---|---|---|

(2011) | 'On stochastic difference equations and applications' Alexandra Rodkina and Cónall Kelly (2011) 'On stochastic difference equations and applications' In: Miodrag Lovric (eds). International Encyclopedia of Statistical Science. Berlin-Heidelberg: Springer-Verlag. [Details] |

### Conference Publications

Year | Publication | |
---|---|---|

(2019) | 23rd International Conference on Difference Equations and Applications (ICDEA 2017)Baccas, Ricardo; Kelly, Cónall; Rodkina, Alexandra (2019) On cubic difference equations with variable coefficients and fading stochastic perturbations 23rd International Conference on Difference Equations and Applications (ICDEA 2017) Timișoara, Romania, , 24-JUL-17 - 28-JUL-17 , pp.171-197 [DOI] [Full Text] [Details] | |

(2009) | The Twelfth International Conference on Difference Equations and ApplicationsJohn A. D. Appleby, Cónall Kelly, and Alexandra Rodkina (2009) Dynamical consistency of solutions of continuous and discrete stochastic equations with a finite time explosion . In: Saber N Elaydi, Henrique Oliveira, José Manuel Ferreira, João F Alves eds. The Twelfth International Conference on Difference Equations and Applications , pp.163-172 [Details] | |

(2007) | IX International Chetayev Conference: Analytical Mechanics, Stability and Control of MotionJohn A. D. Appleby and Cónall Kelly (2007) Almost Sure Asymptotic Behaviour of One- and Two-step Difference Equations with Random Coefficients on a Reducing Mesh IX International Chetayev Conference: Analytical Mechanics, Stability and Control of Motion , pp.318-331 [Details] |

## Professional Activities

### Employment

Employer | Position | From / To | |
---|---|---|---|

University College Cork | College Lecturer in Financial Mathematics | 01-AUG-17 / | |

The University of the West Indies | Head of Department | 01-AUG-14 / 31-JUL-17 | |

The University of the West Indies | Senior Lecturer in Mathematics | 01-AUG-11 / 31-JUL-17 | |

The University of the West Indies | Lecturer in Mathematics | 21-AUG-06 / 31-JUL-11 | |

University College Cork | Postdoctoral Researcher | 15-AUG-05 / 11-AUG-06 |

### Education

Year | Institution | Qualification | Subject | |
---|---|---|---|---|

2005 | Dublin City University | PHD | Mathematical Sciences | |

2019 | UCC | Postgraduate Certificate | Teaching and Learning in Higher Education | |

2001 | Dublin City University | BACHELOR OF SCIENCE HONORS | Mathematical Sciences |

### Honours and Awards

Year | Title | Awarding Body | |
---|---|---|---|

2017 | Outstanding researcher in the Faculty of Science and Technology | The University of the West Indies at Mona. | |

2013 | Outstanding Achievement in Teaching Assessment | Faculty of Science and Technology, The University of the West Indies at Mona. | |

2011 | Outstanding Achievement in Teaching | Faculty of Pure and Applied Sciences, The University of the West Indies at Mona. |

### Professional Associations

Association | Function | From / To | |
---|---|---|---|

Irish Mathematical Society | Treasurer | 01-JAN-20 / | |

European Mathematical Society | Member | / | |

International Society of Difference Equations | Member | / |

### Committees

Committee | Function | From / To | |
---|---|---|---|

SMS Equality, Diversity and Inclusion Committee | Athena SWAN self-assessment team member and leader of the working group on career development | 2021 / | |

SMS BSc Financial Mathematics and Actuarial Science Programme Committee | Mathematics representative | 2020 / | |

International advisory board for conference Emerging Trends in Mathematics for Science and Technology (ETMST-2020), to be held at UWI Mona, Kingston, Jamaica, December 9-11, 2020 (postponed due to COVID-19 outbreak). | Member | 2020 / | |

SMS MSc Financial and Computational Mathematics Programme Committee | Chair | 2020 / | |

Committee of the Irish Mathematical Society | Executive member | 2020 / | |

University Council of Jamaica Committee for Postgraduate Standards in the Natural Sciences and Mathematics | Member | 2019 / | |

Management Committee of the Faculty of Science and Technology, the University of the West Indies at Mona, Jamaica | Member | 2014 / 2017 | |

Academic Board of the University of the West Indies at Mona, Jamaica | Member | 2014 / 2017 | |

Appointments Committee of the Faculty of Science and Technology at the University of the West Indies at Mona, Jamaica | Member | 2014 / 2017 |

### Other Activities

Description | |
---|---|

External assessor for tenure and promotion case, Department of Mathematics, Fordham University, New York, USA. January 2022 | |

External examiner for PhD thesis, Technische Universit ̈at Chemnitz, Germany. September 2021. | |

External examiner for PhD thesis, May 2020, University of Cape Town, South Africa | |

External examiner for 7 MSc Mathematics Dissertations, 2019--2022, at the African Institute for Mathematical Sciences, Mbour, Senegal. | |

External examiner for the School of Mathematics and Statistics, University of Technology, Kingston, Jamaica. March 2017 - present. | |

Member of the University Council of Jamaica Sciences Standards Committee. January 2018 - May 2021. | |

Reviewer of standards for undergraduate degrees in the natural and mathematical sciences for the University Council of Jamaica. June 2017. | |

University Council of Jamaica accreditation team member for the assessment of mathematics programmes at Northern Caribbean University, Mandeville, Jamaica. February 2016. | |

External assessor for academic staff promotion, The University of Guyana, Greater Georgetown, Guyana. December 2015. | |

Quality assurance review team member for the Discipline of Mathematics, UWI Cave Hill, Barbados. March 2012. | |

Reviewer for AMS Mathematical Reviews on MathSciNet |

### Outreach Activities

Description | |
---|---|

In December 2018, as visiting professor, I delivered a course at the African Institute for Mathematical Sciences Mbour, Senegal in Mathematical and Computational Finance as part of their MSc Mathematics. Working with Tom Carroll, also at UCC, we formulated a new block in Mathematical and Computational Finance, which was piloted for students taking the AIMS structured MSc Mathematics in the 20/21 academic year. Now an established part of the programme. | |

In November 2020, served as invited judge of student presentations from groups in the US and Russia for the SIMIODE Challenge Using Differential Equation Modeling, on the topic “Modeling dispute resolution strategies in Sudanese refugee camps”. | |

SEFS UG Graduate of the Year Award. Reviewer of applications for the 2021/22 academic year. | |

From 2017 to present, delivered workshops to intermediate-level secondary school groups participating in the UCC Mathematics Enrichment Programme and students preparing for the Mathematics Olympiad. | |

Tutor, invigilator and marker for the 2010 Jamaican Mathematical Olympiad; judge in the associated UWI Mathematics Problem Solving Competitions 2006/07 and 2007/08. | |

UWI Mathematics Enrichment Programme. In 2007, lead the development and delivery of a programme designed to generate a positive attitude towards mathematics in talented primary school aged children by introducing them to fun mathematical activity on campus. | |

Centre for Talented Youth in Ireland (CTYI). Over 2002-2005, lead the development and delivery of a sequence of mathematics enrichment programmes aimed at groups of children with exceptional abilities, aged be- tween six and sixteen. |

### Conference Contributions

Year | Publication | |
---|---|---|

(2022) | Royal Society of Edinburgh Saltire Research Network Workshop,Cónall Kelly (2022) Numerical methods applied to stochastic differential equations with finite- time explosions. [Invited Lectures (Workshops)], Royal Society of Edinburgh Saltire Research Network Workshop, University of Strathclyde, Glasgow, UK , 29-AUG-22 - 31-AUG-22. [Details] | |

(2022) | International Conference on Scientific Computation and Differential Equations 2022,Cónall Kelly and Gabriel J. Lord (2022) Organisation and chairing of invited minisymposium Time integrators for Applied Stochastic Systems. [Chair Sessions at Symposia], International Conference on Scientific Computation and Differential Equations 2022, University of Iceland , 25-JUL-22 - 29-JUL-22. [Details] | |

(2022) | International Conference on Scientific Computation and Differential Equations 2022,Cónall Kelly (2022) An adaptive splitting method for the Cox-Ingersoll-Ross process. [Invited Oral Presentation], International Conference on Scientific Computation and Differential Equations 2022, University of Iceland , 25-JUL-22 - 25-JUL-22. [Details] | |

(2022) | 27th International Conference on Difference Equations and Applications,Conall Kelly (2022) Adaptivity and splitting for the numerical solution of SDEs with square-root diffusion. [Invited Oral Presentation], 27th International Conference on Difference Equations and Applications, CentraleSuplec-Université, Paris-Saclay, France and Online , 21-JUL-22 - 21-JUL-22. [Details] | |

(2022) | 27th International Conference on Difference Equations and Applications,Cónall Kelly and Elena Braverman (2022) Organiser and chair of Special Session: Stochastic and non-autonomous difference systems. [Chair Sessions at Symposia], 27th International Conference on Difference Equations and Applications, CentraleSuplec-Université, Paris-Saclay, France and online , 20-JUL-22 - 21-JUL-22. [Details] | |

(2022) | 6th Workshop on Stability and Discretisation Issues in Differential Equations,Cónall Kelly (2022) An adaptive splitting method for the Cox-Ingersoll-Ross process. [Plenary Lecture], 6th Workshop on Stability and Discretisation Issues in Differential Equations, Eötvós Loránd University, Budapest, Hungary . [Details] | |

(2022) | RSE Saltire Network Online Seminar,Cónall Kelly (2022) Adaptive timestepping strategies for finite-dimensional SDEs. [Invited Seminars/Guest Lectures], RSE Saltire Network Online Seminar, Virtual, hosted by the University of Strathclyde . [Details] | |

(2021) | AIMS Research Seminar,Cónall Kelly (2021) Stochastic interest rate models and simulation. [Invited Seminars/Guest Lectures], AIMS Research Seminar, Hybrid, hosted by the African Institute for Mathematical Sciences, Mbour, Senegal . [Details] | |

(2021) | Mathematics Seminar, Department of Mathematics,Cónall Kelly (2021) A novel splitting method for the Cox-Ingersoll-Ross model. [Invited Seminars/Guest Lectures], Mathematics Seminar, Department of Mathematics, The University of the West Indies at Mona, Kingston, Jamaica . [Details] | |

(2021) | 26th International Conference on Difference Equations and Applications,Conall Kelly (2021) A new splitting method for the Cox-Ingersoll-Ross process. [Oral Presentation], 26th International Conference on Difference Equations and Applications, University of Sarajevo, Bosnia and Herzegovina . [Details] | |

(2021) | Workshop: Going all online - teaching practice, learning design and assessment,Cónall Kelly (2021) Distributed research groups and remote student supervision. [Invited Lectures (Workshops)], Workshop: Going all online - teaching practice, learning design and assessment, Online, hosted by UCC . [Details] | |

(2021) | 34th Meeting of the Irish Mathematical Society,Cónall Kelly and J.P. McCarthy (2021) Organising committee chair. [Conference Organising Committee Chairperson], 34th Meeting of the Irish Mathematical Society, MTU and online , 02-SEP-21 - 03-SEP-21. [Details] | |

(2020) | Applied Mathematics Seminar,Conall Kelly (2020) Dynamical consistency and adaptivity for stochastic systems. [Invited Seminars/Guest Lectures], Applied Mathematics Seminar, School of Mathematical Sciences, UCC . [Details] | |

(2020) | One World Online Seminar Series: Stochastic Numerics and Inverse Problems,Conall Kelly (2020) A hybrid, adaptive numerical method for the Cox-Ingersoll-Ross model. [Invited Seminars/Guest Lectures], One World Online Seminar Series: Stochastic Numerics and Inverse Problems, Online, hosted by the International Centre for Mathematical Sciences, Edinburgh, UK . [Details] | |

(2019) | International Conference on Scientific Computation and Differential Equations,Conall Kelly and Andrew Steyer (2019) Contributed minisymposium. [Chair Sessions at Symposia], International Conference on Scientific Computation and Differential Equations, Innsbruck, Austria . [Details] | |

(2019) | International Congress on Industrial and Applied Mathematics,Conall Kelly, Gabriel Lord, Heru Maulana, Fandi Sun (2019) Adaptive methods for nonlinear financial models. [Invited Oral Presentation], International Congress on Industrial and Applied Mathematics, Valencia, Spain . [Details] | |

(2019) | International Conference on Scientific Computation and Differential Equations,Conall Kelly, Heru Maulana, Eeva Maria Rapoo, and Alexandra Rodkina (2019) Pathwise stability for the explicit discretisation of nonlinear SDEs with stochastically stabilising diffusion. [Invited Oral Presentation], International Conference on Scientific Computation and Differential Equations, Innsbruck, Austria . [Details] | |

(2019) | International Conference of Numerical Analysis and Applied Mathematics,Conall Kelly (2019) ICNAAM 2019. [Referee], International Conference of Numerical Analysis and Applied Mathematics, Rhodes, Greece . [Details] | |

(2018) | The 24th International Conference on Difference Equations and Applications,Cónall Kelly (2018) Adaptive numerical methods for stochastic systems with non-globally Lipschitz coefficients. [Invited Oral Presentation], The 24th International Conference on Difference Equations and Applications, Dresden, Germany , 21-MAY-18 - 25-MAY-18. [Details] | |

(2018) | Mathematics Seminar, Department of Mathematics and Statistics, UL,Conall Kelly (2018) Adaptive numerical methods for stochastic systems with non-globally Lipschitz coefficients. [Invited Seminars/Guest Lectures], Mathematics Seminar, Department of Mathematics and Statistics, UL, University of Limerick . [Details] | |

(2018) | AIMS Research Seminar,Conall Kelly (2018) Adaptive numerical methods for stochastic models in finance and neuroscience. [Invited Seminars/Guest Lectures], AIMS Research Seminar, African Institute for Mathematical Sciences, Mbour, Senegal . [Details] | |

(2018) | 10th World Congress of the Bachelier Finance Society,Conall Kelly, Gabriel Lord, Eeva Maria Rapoo, Alexandra Rodkina (2018) Adaptive numerical methods for stochastic systems with non-Lipschitz coefficients. [Oral Presentation], 10th World Congress of the Bachelier Finance Society, Trinity College Dublin , 16-JUL-18 - 20-JUL-18. [Details] | |

(2018) | International Conference of Numerical Analysis and Applied Mathematics,Conall Kelly (2018) ICNAAM 2018. [Referee], International Conference of Numerical Analysis and Applied Mathematics, Rhodes, Greece . [Details] | |

(2018) | The 2nd International Conference on Mathematics and Mathematics Education,Cónall Kelly and Gabriel Lord (2018) Stochastic simulation for the pricing of financial derivatives. [Keynote Speaker], The 2nd International Conference on Mathematics and Mathematics Education, Universitas Negeri Padang, Sumatra, Indonesia , 30-JUN-18 - 01-JUL-18. [Details] | |

(2017) | Mathematics Seminar, School of Mathematical Sciences, UCC,Conall Kelly (2017) Adaptive timestepping strategies for nonlinear stochastic systems. [Invited Seminars/Guest Lectures], Mathematics Seminar, School of Mathematical Sciences, UCC, UCC . [Details] | |

(2017) | Probability Seminar, Department of Mathematics, Texas A&M College Station,Conall Kelly (2017) Stabilisation of positive equilibria in population models with noisy prediction based control. [Invited Seminars/Guest Lectures], Probability Seminar, Department of Mathematics, Texas A&M College Station, Texas A&M University at College Station, Texas, USA . [Details] | |

(2017) | CIMPA Research School in Representation Theory and Differential Equations,Conall Kelly (2017) 6 hour short course on Stochastic Difference Equations. [Invited Lectures (Conference)], CIMPA Research School in Representation Theory and Differential Equations, UWI Mona, Kingston, Jamaica . [Details] | |

(2017) | CIMPA Research School in Representation Theory and Differential Equations,C\'onall Kelly, Dmitri Malinin, and Alexandra Rodkina (2017) One-week research school for graduate students. [Conference Organising Committee Member], CIMPA Research School in Representation Theory and Differential Equations, UWI Mona, Kingston, Jamaica . [Details] | |

(2017) | 2017 International Conference on Scientific Computation and Differential Equations,Cónall Kelly (2017) Adaptive timestepping strategies for nonlinear stochastic systems. [Invited Oral Presentation], 2017 International Conference on Scientific Computation and Differential Equations, University of Bath, UK . [Details] | |

(2016) | The 22nd International Conference on Difference Equations and Applications,Cónall Kelly (2016) Stabilisation of difference equations with noisy prediction-based control. [Oral Presentation], The 22nd International Conference on Difference Equations and Applications, Osaka Prefecture University, Japan . [Details] | |

(2015) | SQuaRE Seminar, American Institute of Mathematics,Conall Kelly (2015) Stochastic stability analysis of a reduced galactic dynamo model with perturbed α-effect. [Invited Seminars/Guest Lectures], SQuaRE Seminar, American Institute of Mathematics, AIMS, San José, California, USA . [Details] | |

(2014) | Mathematics Seminar, Department of Mathematics, UWI Mona,Conall Kelly (2014) Lyapunov exponents and stochastic systems. [Invited Seminars/Guest Lectures], Mathematics Seminar, Department of Mathematics, UWI Mona, The University of the West Indies at Mona, Kingston, Jamaica . [Details] | |

(2014) | Scientific Computation and Industrial Mathematics Seminar, The University of Nottingham,Conall Kelly (2014) Almost sure properties of some discrete-time stochastic systems. [Invited Seminars/Guest Lectures], Scientific Computation and Industrial Mathematics Seminar, The University of Nottingham, Nottingham, UK . [Details] | |

(2014) | Mathematics Seminar, Department of Mathematical Sciences, The University of Bath,Conall Kelly (2014) Almost sure properties of some discrete-time stochastic systems. [Invited Seminars/Guest Lectures], Mathematics Seminar, Department of Mathematical Sciences, The University of Bath, Bath, UK . [Details] | |

(2014) | SQuaRE Seminar at the American Institute of Mathematics,Conall Kelly (2014) Some examples of stochastic stabilisation. [Invited Lectures (Conference)], SQuaRE Seminar at the American Institute of Mathematics, AIMS, Palo Alto, California, USA . [Details] | |

(2014) | Kyoto Conference on Numerical Analysis and Differential Equations,Cónall Kelly (2014) Polynomial difference equations under stochastic perturbation. [Oral Presentation], Kyoto Conference on Numerical Analysis and Differential Equations, Kyoto University Rakuyu-Kaikan, Japan . [Details] | |

(2014) | Mathematics Seminar, Institut für Mathematik, Humboldt Universität zu Berlin,Conall Kelly (2014) Stochastic systems with nonnormal drift. [Invited Seminars/Guest Lectures], Mathematics Seminar, Institut für Mathematik, Humboldt Universität zu Berlin, Berlin, Germany . [Details] | |

(2014) | Probability and Statistics Research Seminar, The University of Manchester,Conall Kelly (2014) Stochastic systems with nonnormal drift. [Invited Seminars/Guest Lectures], Probability and Statistics Research Seminar, The University of Manchester, Manchester, UK . [Details] | |

(2013) | SIAM Conference on Applications of Dynamical Systems,Cónall Kelly (2013) Stochastic effects in non-normal systems: an example from ecology. [Invited Oral Presentation], SIAM Conference on Applications of Dynamical Systems, Snowbird Ski and Summer Resort, Utah, USA . [Details] | |

(2013) | 2013 International Conference on Scientific Computation and Differential Equations,Cónall Kelly (2013) On the use of discrete forms of the Itô formula. [Invited Oral Presentation], 2013 International Conference on Scientific Computation and Differential Equations, University of Valladolid, Spain . [Details] | |

(2013) | 2nd Austrian Stochastics Day, ÖMG-DMV Congress 2013,Cónall Kelly (2013) Response to low-intensity stochastic perturbation in non-normal dynamical systems. [Invited Oral Presentation], 2nd Austrian Stochastics Day, ÖMG-DMV Congress 2013, University of Innsbruck, Austria . [Details] | |

(2013) | CARISCIENCE Conference and AGM,Cónall Kelly (2013) Randomness, stability, and transience in mathematical models. [Oral Presentation], CARISCIENCE Conference and AGM, Runaway Bay, Jamaica . [Details] | |

(2012) | First School in Applied Mathematics,Davide Batic, C\'onall Kelly, Alexandra Rodkina (2012) Workshop and research school for graduate students. [Conference Organising Committee Member], First School in Applied Mathematics, UWI Mona, Kingston, Jamaica . [Details] | |

(2012) | Numerical Solution of Differential and Differential-Algebraic Equations (NUMDIFF-13),Cónall Kelly (2012) Non-normal drift structures and linear stability analysis of numerical methods for systems of stochastic differential equations. [Oral Presentation], Numerical Solution of Differential and Differential-Algebraic Equations (NUMDIFF-13), Martin-Luther-University Halle-Wittenberg, Halle, Germany . [Details] | |

(2012) | 9th Conference of the Faculty of Pure and Applied Sciences,Paul Aiken, Chair and other committee members (2012) Faculty conference. [Conference Organising Committee Member], 9th Conference of the Faculty of Pure and Applied Sciences, UWI Mona, Kingston, Jamaica . [Details] | |

(2011) | Progress on Difference Equations,Cónall Kelly (2011) Destabilising effects in linear stochastic systems and the θ-Maruyama method. [Oral Presentation], Progress on Difference Equations, Dublin City University, Ireland . [Details] | |

(2011) | 2011 Workshop in Stochastic and Deterministic Partial Differential Equations,Davide Batic, Conall Kelly, Nagarani Ponakala (2011) Workshop with invited speakers. [Invited Lectures (Conference)], 2011 Workshop in Stochastic and Deterministic Partial Differential Equations, UWI Mona, Kingston, Jamaica . [Details] | |

(2011) | Mathematics Seminar, UWI at Mona,Conall Kelly (2011) Destabilising perturbations and numerical methods for stochastic differen- tial equations. [Invited Seminars/Guest Lectures], Mathematics Seminar, UWI at Mona, The University of the West Indies at Mona . [Details] | |

(2010) | 8th AIMS International Conference on Dynamical Systems and Differential Equations,Cónall Kelly (2010) On the implications of feedback geometry for stochastic numerical methods. [Invited Oral Presentation], 8th AIMS International Conference on Dynamical Systems and Differential Equations, Dresden University of Technology, Germany . [Details] | |

(2010) | 8th AIMS Conference on Dynamical Systems, Differential Equations and Applications,Conall Kelly and Alexandra Rodkina (2010) Special Session ‘Perturbed Difference and Differential Equations’. [Chair Sessions at Symposia], 8th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Dresden University of Technology, Germany . [Details] | |

(2010) | XVII International Symposium on Mathematical Methods Applied to the Sciences,Cónall Kelly (2010) On the implications of feedback geometry for stochastic numerical methods. [Plenary Lecture], XVII International Symposium on Mathematical Methods Applied to the Sciences, University of Costa Rica, San Jose, Costa Rica . [Details] | |

(2010) | TWAS-ROLAC Caribbean Young Scientist & Technologist Conference,Cónall Kelly (2010) On the implications of feedback geometry for stochastic numerical methods. [Oral Presentation], TWAS-ROLAC Caribbean Young Scientist & Technologist Conference, Ocho Rios, Jamaica . [Details] | |

(2009) | Warwick Mathematics Institute,Conall Kelly (2009) Local Dynamics of Stochastic Difference Equations. [Invited Seminars/Guest Lectures], Warwick Mathematics Institute, The University of Warwick, Coventry, UK . [Details] | |

(2009) | Seventh ISAAC Congress,Cónall Kelly (2009) Evaluating the Stochastic Theta Method. [Invited Oral Presentation], Seventh ISAAC Congress, Imperial College London, UK . [Details] | |

(2009) | Department of Mathematics and Statistics Seminar, University of Strathclyde,Conall Kelly (2009) Local Dynamics of Stochastic Difference Equations. [Invited Seminars/Guest Lectures], Department of Mathematics and Statistics Seminar, University of Strathclyde, Glasgow, UK . [Details] | |

(2009) | Heriot-Watt University Computational Mathematics and Mathematical Biology Seminar,Conall Kelly (2009) Linear stability analysis of one-step methods for systems of stochastic differential equations. [Invited Seminars/Guest Lectures], Heriot-Watt University Computational Mathematics and Mathematical Biology Seminar, Edinburgh, UK . [Details] | |

(2009) | Seminar of the School of Mathematical Sciences, DCU,Conall Kelly (2009) Linear Stability Analysis of One-Step Methods for Systems of Stochastic Dif- ferential Equations. [Invited Seminars/Guest Lectures], Seminar of the School of Mathematical Sciences, DCU, Dublin, Ireland . [Details] | |

(2009) | 2009 International Conference on Scientific Computation and Differential Equations,Cónall Kelly (2009) Linear Stability Analysis of One-Step Methods for Systems of Stochastic Differential Equations. [Invited Oral Presentation], 2009 International Conference on Scientific Computation and Differential Equations, Beijing, China . [Details] | |

(2008) | Mathematics Seminar, UWI at Mona,Conall Kelly (2008) Local Convergence of Difference Equations with Fading Gaussian Noise. [Invited Seminars/Guest Lectures], Mathematics Seminar, UWI at Mona, Kingston, Jamaica . [Details] | |

(2008) | Heriot-Watt University Mathematics Seminar,Conall Kelly (2008) Local Stability of Polynomial Difference Equations Experiencing Unbounded Stochastic Perturbations. [Invited Seminars/Guest Lectures], Heriot-Watt University Mathematics Seminar, Edinburgh, UK . [Details] | |

(2008) | University of Puerto Rico Mathematics Seminar,Conall Kelly (2008) Local Convergence of Difference Equations with Fading Gaussian Noise. [Invited Seminars/Guest Lectures], University of Puerto Rico Mathematics Seminar, Mayagüez, Puerto Rico . [Details] | |

(2008) | Seventh AIMS International Conference on Dynamic Systems and Differential Equations,Cónall Kelly (2008) Discretising a Polynomial Differential Equation with Fading Stochastic Perturbation. [Invited Oral Presentation], Seventh AIMS International Conference on Dynamic Systems and Differential Equations, University of Texas, Arlington, TX, USA . [Details] | |

(2008) | IX International Conference: Approximation and Optimization in the Caribbean,Cónall Kelly (2008) Explosions and Hard Landings in Discretized Nonlinear Stochastic Equations. [Invited Oral Presentation], IX International Conference: Approximation and Optimization in the Caribbean, San Andrés Island, Colombia . [Details] | |

(2008) | Eighth Conference: Faculty of Pure and Applied Sciences,Cónall Kelly (2008) Feedback Noise in Dynamical Systems. [Oral Presentation], Eighth Conference: Faculty of Pure and Applied Sciences, University of the West Indies, Kingston, Jamaica . [Details] | |

(2007) | Workshop on Stochastic Differential Equations and their Applications,Cónall Kelly (2007) Nonlinear Stochastic Functional Differential Equations: Stabilisation and Destabilisation. [Invited Lectures (Workshops)], Workshop on Stochastic Differential Equations and their Applications, University of Strathclyde, Glasgow, UK . [Details] | |

(2007) | IX International Chetayev Conference: Analytical Mechanics, Stability and Control of Motion,Cónall Kelly (2007) Consistency in the Oscillatory Dynamics of Discrete and Continuous Stochastic Equations. [Invited Oral Presentation], IX International Chetayev Conference: Analytical Mechanics, Stability and Control of Motion, The Institute for System Dynamics and Control Theory, Siberian Branch, Russian Academy of Sciences, Irkutsk, Russian Federation . [Details] | |

(2007) | 12th International Conference on Difference Equations and Applications,Cónall Kelly (2007) Dynamical Consistency in Discrete and Continuous Equations with Finite-Time Explosions. [Invited Oral Presentation], 12th International Conference on Difference Equations and Applications, Instituto Superior Tecnico, Technical University of Lisbon, Portugal . [Details] | |

(2007) | School of Mathematical Science Seminar, DCU,Conall Kelly (2007) Explosions in Discrete Time. [Invited Seminars/Guest Lectures], School of Mathematical Science Seminar, DCU, Dublin, Ireland . [Details] | |

(2006) | University of Strathclyde Lunchtime Seminar,Conall Kelly (2006) Stochastic Delay Differential Equations with Highly Nonlinear Coefficients: Oscillation. [Invited Seminars/Guest Lectures], University of Strathclyde Lunchtime Seminar, Glasgow, UK . [Details] | |

(2006) | Mathematics Seminar, UWI at Mona,Conall Kelly (2006) Nonlinearity and Random Dynamics. [Invited Seminars/Guest Lectures], Mathematics Seminar, UWI at Mona, Kingston, Jamaica . [Details] | |

(2006) | Conference on Differential and Difference Equations and Applications,Cónall Kelly (2006) Complementary Theoretical and Numerical Analysis of a Perturbed Geometric Brownian Motion. [Oral Presentation], Conference on Differential and Difference Equations and Applications, Rajecké Teplice, Slovak Republic . [Details] | |

(2005) | Algorithms for Approximation V,Cónall Kelly (2005) A Uniform Euler Discretisation of the Linear Stochastic Vanishing Delay Equation Yields Spurious Oscillatory Behaviour. [Oral Presentation], Algorithms for Approximation V, Chester College, UK . [Details] | |

(2005) | Applied Mathematics Seminar, UCC,Conall Kelly (2005) The Oscillatory Behaviour of Stochastic Delay Equations. [Invited Seminars/Guest Lectures], Applied Mathematics Seminar, UCC, Cork, Ireland . [Details] | |

(2005) | Workshop on Computational Stochastic Differential Equations,Cónall Kelly (2005) Discrete Models of the Stochastic Vanishing Delay Equation. [Invited Oral Presentation], Workshop on Computational Stochastic Differential Equations, Mathematical Research and Conference Centre, Bedlewo, Poland . [Details] | |

(2004) | Joint Meeting of the 56th British Mathematical Colloquium and the 17th Annual Meeting of the Irish Mathematical Society,Cónall Kelly (2004) Preventing Explosions in the Solutions of Functional Differential Equations by Noise Perturbation. [Oral Presentation], Joint Meeting of the 56th British Mathematical Colloquium and the 17th Annual Meeting of the Irish Mathematical Society, Queen’s University, Belfast, N. Ireland . [Details] | |

(2004) | World Congress of Nonlinear Analysts,Cónall Kelly (2004) Stochastic Difference and Differential Equations with Vanishing Delay. [Invited Lectures (Conference)], World Congress of Nonlinear Analysts, Orlando, USA . [Details] | |

(2003) | Research Students’ Conference in Probability and Statistics,Cónall Kelly (2003) The Asymptotic Behaviour of Stochastic Delay Differential Equations. [Oral Presentation], Research Students’ Conference in Probability and Statistics, University of Surrey, UK . [Details] |

### Journal Activities

Journal | Role | To / From | |
---|---|---|---|

Discrete And Continuous Dynamical Systems-Series B | Referee | - | |

Mathematics Of Computation | Referee | - | |

Ima Journal Of Numerical Analysis | Referee | - | |

Numerische Mathematik | Referee | - | |

Siam Journal On Scientific Computing | Referee | - | |

Bit Numerical Mathematics | Referee | - | |

International Journal Of Computer Mathematics | Referee | - | |

Applied Numerical Mathematics | Referee | - | |

Siam/Asa Journal On Uncertainty Quantification | Referee | - | |

Journal Of Mathematical Analysis And Applications | Referee | - | |

Mathematics And Computers In Simulation | Referee | - | |

Numerical Algorithms | Referee | - | |

Journal Of Computational And Applied Mathematics | Referee | - | |

Discrete And Continuous Dynamical Systems-Series S | Referee | - |

## Teaching Activities

### Teaching Interests

__Academic Year 2022/23__

*Semester 1:*

__MF3052 (MF6011) Derivatives, Securities and Option Pricing__

MF4052 (MF6012) Computational Finance I

*Semester 2 and Summer:*

Sabbatical leave

In the past I have also taught modules in Probability Theory, Statistical Inference, Stochastic Modelling, Differential Equations, Mathematical Analysis , Numerical Analysis, Complex Analysis, Time Series Analysis, Measure and Integration, Stochastic Difference Equations, Elementary Number Theory, and Business Mathematics.

As visiting professor, I have taught at Johannes Kepler University, Linz, Austria, and the African Institute of Mathematical Sciences, Mbour, Senegal, and had the chance to give short courses to graduate students at Universitas Negeri Padang, Indonesia, and as part of a CIMPA Research School hosted by UWI, Jamaica.

I have supervised undergraduate final year projects both at UWI and UCC, mentoring 9 students between 2013 and 2021, and over the Summer of 2022 I superved one of our Boole interns here in the School of Mathematical Sciences at UCC, conducting research in the area of computational finance.

__Current research students (external)__

Fandi Sun, PhD Mathematics, Heriot-Watt University, Edinburgh, UK.

Project:

*Adaptive time-stepping strategies for stochastic differential equations with Milstein scheme.*

### Recent Postgraduates

Graduation Year | Student Name | Institution | Degree Type | Thesis Title | |
---|---|---|---|---|---|

2022 | Heru Maulana | University College Cork | PHD | The role of adaptivity in a numerical method for the Cox-Ingersoll-Ross model | |

2023 | Abhishek Sharma | University College Cork | (MSc Financial and Computational Mathematics) Local volatility models and the Open Source Risk Project | ||

2022 | Christopher Noonan | University College Cork | (MSc Financial and Computational Mathematics) The SABR stochastic volatility model and the Open Source Risk project. | ||

2022 | Arinjoy Bhanja | University College Cork | (MSc Financial and Computational Mathematics) Implied volatility and calibration of the SABR volatility model. | ||

2022 | Isaac Kobby Anni | African Institute for Mathematical Sciences | MSc Mathematics | Structural approach to credit risk modelling. | |

2021 | Ciaran O'Connor | University College Cork | (MSc Financial and Computational Mathematics) Electricity Price Forecasting using Machine Learning Methods | ||

2021 | Anguo Bu | University College Cork | (MSc Financial and Computational Mathematics) Modelling Forward LIBOR Rates and the Pricing of Caplets | ||

2020 | Joy Agwu Onyekachi | African Institute for Mathematical Sciences | MSc Mathematics | Valuation of financial derivatives via the solution of partial differential equations | |

2019 | Ricardo Baccas | The University of the West Indies at Mona. | MPH | On stability of difference equations with variable coefficients and fading stochastic perturbations | |

2019 | Irene Muia Mbeke | African Institute for Mathematical Sciences | MSc Mathematics | Monte Carlo option valuation using multilevel variance reduction techniques | |

2018 | Stephen Barnes | The University of the West Indies at Mona. | MPH | Stochastic Models for Structured Financial Products: Theoretical Background and Multilevel Monte-Carlo Simulation | |

2017 | Damian Welsh | The University of the West Indies at Mona. | MSc Mathematics | Common stochas- tic models for short-term interest rates and an application of the Cox-Ingersoll Ross model. | |

2016 | Andrene Salmon | The University of the West Indies at Mona. | MSc Mathematics | Solving stochas- tic differential equations: a theoretical and numerical approach. | |

2016 | Tricia Morris | The University of the West Indies at Mona. | MSc Mathematics | Systems of stochastic differential equations and their simulation | |

2016 | Oma Coke | The University of the West Indies at Mona. | MSc Mathematics | Selected stochastic differential equation models with applications in finance | |

2014 | Peter Palmer | The University of the West Indies at Mona. | PHD | Almost sure asymptotic stability of the equilibria of discretisations of stochastic differential equations. | |

2013 | Kimberly Boswell | The University of the West Indies at Mona. | MSc Mathematics | Simulating stock price movements and option pricing under risk neutral probability. | |

2012 | Michelle Wilson | The University of the West Indies at Mona. | MSc Mathematics | Simulation of the properties of Brownian motion | |

2008 | Kirk Morgan | The University of the West Indies at Mona. | MPH | On stability of difference equations of non-hyperbolic type. |

## Research Information

### External Collaborators

Name | Organisation / Institute | Country | |
---|---|---|---|

Xuerong Mao | University of Strathclyde | SCOTLAND | |

Gabriel Lord | Radboud University | HOLLAND | |

Elena Braverman | University of Calvary | CANADA | |

Alexandra Rodkina | The University of the West Indies | JAMAICA | |

Eeva Maria Rapoo | The University of South Africa | SOUTH AFRICA | |

Gregory Berkolaiko | Texas A&M University | U.S.A. |