Research Profile

Conall Kelly

Biography

I completed my PhD in 2005 at Dublin City University with a thesis entitled "On the oscillatory behaviour of stochastic delay differential equations", after which I spent a year at University College Cork as a postdoc in the SFI funded Probability Group, Department of Mathematics / BCRI.

In August 2006 I moved to the Mona campus of the University of the West Indies in Kingston, Jamaica, where I spent eleven years before returning to Ireland to take a position at UCC in August 2017.

Google Scholar profile.
Publications indexed on MathSciNet.
Reviews published on MathSciNet.

Research Interests

Stochastic difference and differential equations;
Numerical methods for stochastic differential equations;
Applications including in finance.

Research Grants

 ProjectFunding
Body
Start DateEnd DateAward
College of SEFS Start-up fund.Miscellaneous01-SEP-1731-AUG-20€2,500.00
Stochastic models for employee stock optionsOther: Not Listed01-OCT-1720-SEP-20€81,000.00

Publications

Peer Reviewed Journals

 YearPublication
(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

 YearPublication
(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

 YearPublication
(2019)The 23rd International Conference on Difference Equations and Applications (ICDEA 2017)
Ricardo Baccas, Cónall Kelly, and Alexandra Rodkina (2019) On cubic difference equations with variable coefficients and fading stochastic perturbations The 23rd International Conference on Difference Equations and Applications (ICDEA 2017) [Details]
(2009)The Twelfth International Conference on Difference Equations and Applications
John 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 Motion
John 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

Honours and Awards

 YearTitleAwarding Body
2017Most outstanding researcher in the Faculty of Science and Technology The University of the West Indies at Mona.
2013Outstanding Achievement in Teaching Assessment Faculty of Science and Technology, The University of the West Indies at Mona.
2011Outstanding Achievement in Teaching Faculty of Pure and Applied Sciences, The University of the West Indies at Mona.

Professional Associations

 AssociationFunctionFrom / To
Bachelier Finance Society Member/
American Mathematical Society Member/
International Society of Difference Equations Member/

Education

 YearInstitutionQualificationSubject
2005Dublin City University PHDMathematical Sciences
2001Dublin City University BACHELOR OF SCIENCE HONORSMathematical Sciences

Employment

 EmployerPositionFrom / To
University College Cork Lecturer in Financial Mathematics01-AUG-17 /
The University of the West Indies Head of Department01-AUG-14 / 31-JUL-17
The University of the West Indies Senior Lecturer in Mathematics01-AUG-11 / 31-JUL-17
The University of the West Indies Lecturer in Mathematics21-AUG-06 / 31-JUL-11
University College Cork Postdoctoral Researcher15-AUG-05 / 11-AUG-06

Other Activities

 Description

Member of the University Council of Jamaica Sciences Standards Committee. January 2018 - present.

External examiner for three MSc Mathematics Dissertations, February 2019, 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.

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.

Conference Contributions

 YearPublication
(2018)The 24th International Conference on Difference Equations and Applications,
Cónall Kelly (2018) ICDEA2018. [Invited Oral Presentation], The 24th International Conference on Difference Equations and Applications, Dresden, Germany , 21-MAY-18 - 25-MAY-18. [Details]
(2018)10th World Congress of the Bachelier Finance Society,
Conall Kelly, Gabriel Lord, Eeva Maria Rapoo, Alexandra Rodkina (2018) Bachelier 2018. [Oral Presentation], 10th World Congress of the Bachelier Finance Society, Trinity College Dublin , 16-JUL-18 - 20-JUL-18. [Details]
(2018)The 2nd International Conference on Mathematics and Mathematics Education,
Cónall Kelly and Gabriel Lord (2018) ICM2E 2018. [Keynote Speaker], The 2nd International Conference on Mathematics and Mathematics Education, Universitas Negeri Padang, Sumatra, Indonesia , 30-JUN-18 - 01-JUL-18. [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]
(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]
(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)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)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)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)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]
(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]
(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]
(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)XVII International Symposium on Mathematical Methods Applied to the Sciences,
Cónall Kelly (2010) On the implications of feedback geometry for stochastic numerical methods. [Invited Lectures (Conference)], XVII International Symposium on Mathematical Methods Applied to the Sciences, University of Costa Rica, San Jose, Costa Rica . [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]
(2009)Seventh ISAAC Congress,
Cónall Kelly (2009) Evaluating the Stochastic Theta Method. [Invited Oral Presentation], Seventh ISAAC Congress, Imperial College London, UK . [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]
(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)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]
(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]
(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

 JournalRoleTo / From
Discrete And Continuous Dynamical Systems-Series B 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

Semester 1, 2018/19

MF3052 Derivatives, Securities and Option Pricing
MF4052 Computational Finance

Semester 2, 2018/19

MA1100 Introductory Mathematics for Business I
MA2054 Ordinary Differential Equations
MF4090 Project in Financial Mathematics

As visiting professor, December 2019

Mathematical and Computational Finance, MSc Mathematics, African Institute for Mathematical Sciences, Mbour, Senegal.

Current graduate students (internal)

  • Heru Maulana, PhD Financial Mathematics, UCC.
    • Status: ongoing.
    • Project: Stochastic Models for employee stock options.
Current graduate students (external)

  • Fandi Sun, PhD Mathematics, Heriot-Watt University, Edinburgh, UK.
    • Status: ongoing.
    • Project: Adaptive time-stepping strategies for stochastic differential equations with Milstein scheme. 
  • Irene Muia, MSc Mathematics, African Institute for Mathematical Sciences, Mbour, Senegal.
    • Status: ongoing.
    • Project: Monte Carlo option valuation using multilevel variance reduction techniques.
  • Ricardo Baccas, MPhil Mathematics, The University of the West Indies at Mona, Jamaica. 
    • Status: submitted. 
    • Project: Local stability and instability of polynomial stochastic difference equations. 


Recent Postgraduates

 Graduation YearStudent NameInstitutionDegree TypeThesis Title
2018Stephen Barnes The University of the West Indies at Mona.MPHStochastic Models for Structured Financial Products: Theoretical Background and Multilevel Monte-Carlo Simulation
2014Peter Palmer The University of the West Indies at Mona.PHDAlmost sure asymptotic stability of the equilibria of discretisations of stochastic differential equations.
2008Kirk Morgan The University of the West Indies at Mona.MPHOn stability of difference equations of non-hyperbolic type.

Research Information

External Collaborators

 NameOrganisation / InstituteCountry
Eeva Maria Rapoo The University of South AfricaSOUTH AFRICA
Elena Braverman University of CalvaryCANADA
Alexandra Rodkina The University of the West IndiesJAMAICA
Gregory Berkolaiko Texas A&M UniversityU.S.A.
Gabriel Lord Heriot-Watt UniversityUNITED KINGDOM

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