1. Option Pricing: Mathematical Models and Computation (with J.N. Dewynne & P. Wilmott). Oxford Financial Press 1993.
2. Mathematical Models in Finance (edited with F.P. Kelly and P. Wilmott). Chapman & Hall 1995.
3. Mathematical Models of Financial Derivatives: a Student Introduction (with P. Wilmott & J.N. Dewynne). Cambridge University Press 1995.
4. Applied Partial Differential Equations (with J.R. Ockendon, A.A. Lacey & A.B. Movchan). Oxford University Press 1999 (revised edition, 2003).
5. Practical Applied Mathematics: Modelling, Analysis, Approximation, Cambridge University Press, in production, 2004.
76. Limit Order
Books, Quantitative Finance 13, 1709-1742, 2013 (with D. Fenn, M. Gould, M.
MacDonald, M.A. Porter & S. Williams) (available here).
65. The mirage of triangular arbitrage in the spot foreign exchange market, in press, IJTAF 12, 1105-1123, 2009 (with D. Fenn, S. Williams & N.F. Johnson) (PDF here).
64. Impact of unexpected events, shocking news, and
exchange market dynamics. Phys. Rev. E 77,
S. Williams & N.F. Johnson).
62. The motion of a viscous filament in a porous medium or Hele-Shaw cell: a physical realisation of the Cauchy-Riemann Equations. Applied Math. Letters 19, 356-361, 2006 (with C.L. Farmer) (pdf here).
61. A matched asymptotic expansions approach to continuity corrections for discretely sampled options. Part 2: Bermudan options. Applied Mathematical Finance, 14, 91-104, 2007. (PDF here.)
60. A matched asymptotic expansions approach to continuity corrections for discretely sampled options. Part 1: Barrier options. Applied Mathematical Finance 14, 63-89, 2007 (with Mario Steinberg). (PDF here.)
59. A class of exactly solvable free boundary inhomogeneous porous medium flows, Applied Math. Letters 20, 93-97, 2007 (with I. Loutsenko & J.R. Ockendon). (PDF here.)
58. Detecting a currency's dominance or dependence using foreign exchange network trees, Phys. Rev. E 72, 046106, 2005 (with M. McDonald, O. Suleman, S. Williams & N.F. Johnson).
57. Droplet impact on a thin fluid layer, J. Fluid. Mech. 542, 1-23, 2005 (with J.R. Ockendon, J.M. Oliver, R. Purvis & F.T. Smith). (PDF here.)
56. Matched asymptotic expansions in financial engineering, J. Eng. Math. 53, 385-406, 2005 (James Lighthill Memorial Paper). (PDF here.)
55. Ray methods for free boundary problems, Quart. Appl. Math. 64, 41-59, 2006 (with J.A. Addison & J.R. King). (PDF here.)
53. A free boundary problem arising in a model for shallow water entry at small deadrise angles, Europ. J. Appl. Math. 15, 839-851, 2004 (with J.M. Oliver). (PDF here.)
52. Pricing and hedging of volatility derivatives, Applied Math. Finance 11, 317-348, 2004 (with A. Rafailidis & H. Rasmussen). (PDF here.)
51. Global existence, singular solutions and ill-posedness for the Muskat problem, Comm. Pure Appl. Math. LVII, 1-38, 2004 (with M.J. Siegel & R.E. Caflisch). (PDF here.)
50. Using Greeks of options as liquidity protection, Derivatives Trading, Use & Regulation 9, 234-245, 2004 (with D. Bakstein). (PDF here.)
49. Mushy regions in negative squeeze films, Quart. J. Mech. Appl. Math. 56, 361-379, 2003 (with A.A. Lacey & J.R. Ockendon). (PDF here.)
48. Oblique slamming, planning and skimming, J. Eng. Math. 48, 321-337, 2004 (with J.M. Oliver & J.R.Ockendon). (PDF here.)
47. Deep- and shallow-water slamming at small and zero deadrise angles, J. Eng. Math. 42, 373-388, 2002 (with J.M. Oliver & J.R. Ockendon). (PDF here.)
46. Application of multi-agent games to the prediction of financial time series, Physica A 299, 222-227, 2001 (with N.F. Johnson, D. Lamper, P. Jefferies & M.L. Hart).
45. Predictability of large future changes in a competitively evolving population, Phys. Rev. Lett. 88 017902, 2002 (with N.F. Johnson & D. Lamper). (PDF here.)
44. Trading volume in models of financial derivatives, Applied Mathematical Finance 8, 119-135, 2001 (with David Lamper).
43. A note on the two-phase Hele-Shaw problem, J. Fluid Mech. 409, 243-249, 2000.
42. Two-dimensional Stokes flow with suction and small surface tension, Europ. J. Appl. Math. 10, 681-706, 1999 (with L.J. Cummings). (PDF here.)
41. Two-dimensional Stokes and Hele-Shaw flow with free surfaces, Europ. J. Appl. Math. 10, 635-680, 1999 (with L.J. Cummings & J.R. King). (PDF here.)
40. Two-dimensional solidification and melting in Darcy flow, J. Fluid Mech. 378, 1-18, 1999 (with L.J. Cummings, Yu.E. Hohlov & K. Kornev). (PDF here.)
39. Computation of deterministic volatility surfaces, J. Comp. Finance 2, 5-32, 1999 (with E. Suli & N.A. Jackson).
38. Dynamics of line singularities, Phil. Trans. Roy. Soc. 355, 2013-2024, 1997 (with A. Carpio, S.J. Chapman & J.R. Ockendon).
37. Numerical and asymptotic solution of a sixth-order nonlinear diffusion equation and related coupled systems, I. M .A. J. Appl. Math. 57, 79-98, 1996 (with W.R. Smith & D.F. Mayers).
36. A mathematical model for drying paint layers, J. Eng. Math. 32, 377-394, 1997 (with J. Moriarty, J.R. Ockendon, L. Terrill & S.K. Wilson).
35. Conserved quantities in Stokes flow with free surfaces, Phys. Fluids 9, 477-480, 1997 (with L.J. Cummings & J.R. King).
34. Asymptotics of violent surface motion, Phil. Trans. Roy. Soc. 355, 679-685, 1997 (with S.J. Chapman, K.A. Gillow & J.R. Ockendon).
33. A class of codimension two free boundary problems, SIAM Review 39, 221-253, 1997 (with J.D. Morgan & J.R. Ockendon).
30. Applied mathematics and finance, Phil. Trans Roy. Soc. A347, 465-470, 1994.
27. Some mathematical results in the pricing of American Options, Europ. J. Appl. Math. 4, 381-398, 1993 (with J.N. Dewynne, I. Rupf & P. Wilmott).
26. A model for Hele-Shaw flows with non-smooth free boundaries, Quart. J. Mech. Appl. Math. 47, 107-128, 1994 (with Yu. E. Hohlov, C. Huntingford, A.A. Lacey & J.R. Ockendon).
25. O klassifikatsii reshenii v zadache o techeniyakh Khele-Shou s neizvestnoi granitsei, Dokl. Rossiiskoi Akad. Nauk. 325, 1161-1166, 1992 (with Yu. E. Hohlov).
24. Fluorescent transfer of light in dyed materials, SIAM J. Appl. Math. 53, 447-458, 1993 (with R.J. Lawrence).
23. On the classification of solutions to the zero-surface-tension Hele-Shaw problem, Quart. Appl. Math 51, 777-789, 1993 (with Yu.E. Hohlov).
22. Macroscopic models for superconductivity, SIAM Review 34, 529-560, 1992 (with S.J. Chapman & J.R. Ockendon).
modelling of dislocation plasticity, Physica Scripta T44,
1992 (with A.K. Head, J.R. Ockendon & S.P. Tighe).
20. Complex variable methods in Hele-Shaw moving boundary problems, Europ. J. Appl. Math. 3, 209-224 (1992).
19. Normal-superconducting transitions in Landau-Ginzburg theory, Proc. Roy. Soc. Edinburgh 119A, 117-124, 1991 (with S.J. Chapman, J.B. McLeod & J.R. Ockendon).
18. Stationary solutions to the thermistor problem, J. Math Anal. Applics 174, 573-588, 1993 (with M. Shillor & J.-F. Rodrigues).
17. Irregular morphologies in unstable Hele-Shaw free boundary problems, Quart. J. Mech. Appl. Math. 43, 387-405, 1990 (with A.A. Lacey, J.R. Ockendon & P. Wilmott).
16. Inviscid water entry problems at small deadrise angles, J. Fluid Mech. 222, 215-230, 1991 (with J.R. Ockendon & S.K. Wilson).
15. Temperature surges in current-limiting circuit devices, SIAM J. Appl. Math. 52, 998-1011, 1992 (with A.C. Fowler & I. Frigaard).
14. Some remarks on the regularisation of supercooled Stefan problems in one space dimension, Quart. Appl. Maths 48, 153-168, 1990 (with A. Fasano, M. Primicerio & J.R. Ockendon).
behaviour of solutions to the Stefan problem with a kinetic condition
free boundary, J. Aust. Math. Soc. Ser. B, 31, 81-96, 1989
J.N. Dewynne, J.R. Ockendon & W. Xie).
11. Explicit solutions to six free boundary problems in fluid flow and diffusion, I. M. A. J. Appl. Maths 42, 155-175, 1989 (with J.R. King).
10. Similarity solutions to the Stefan problem and the binary alloy problem, I. M. A. J. Appl. Maths 40, 147-161, 1988.
9. Slot suction from inviscid channel flow, J. Fluid Mech. 200, 265-282, 1989 (with J. Dewynne, L.C. Morland, J.R. Ockendon & E. J. Watson).
7. Existence and stability for spherical crystals growing in a supersaturated solution, I. M. A. J. Appl. Maths 39, 1-15, 1987 (with J. Chadam & P. Ortoleva).
6. A continuum model for two-dimensional dislocation distributions, Phil. Mag. 55A, 617-629, 1987 (with A.K. Head, J.R. Ockendon, J.B. Titchener & P. Wilmott).
5. Fingering in Hele-Shaw cells, J. Fluid Mech. 167, 439-453, 1986.
4. Bubble growth in porous media and Hele-Shaw cells, Proc. Roy. Soc. Edinburgh 102A, 141-148, 1986.
1. Mathematical Models in Finance, proceedings of a Royal Society Discussion Meeting, Phil. Trans. Roy. Soc. 347, 449-598, 1994 (with F.P. Kelly FRS & P. Wilmott).
2. Violent Surface Motion, proceedings of a Royal Society Discussion Meeting, Phil. Trans. Roy. Soc. 355, 487-689, 1997 (with J.R. Ockendon FRS, D.H. Peregrine & D.W. Moore FRS.
3. Vortices, Dislocations and line singularities in Partial Differential Equations, proceedings of a Royal Society Discussion Meeting, Phil. Trans. Roy. Soc. 355, 1945-2072, 1997 (with S.J. Chapman, C.M. Elliott, A.K. Head FRS, F.M. Leslie, & J.R. Ockendon FRS).
4. Mathematics in Finance, themed issue of Phil. Trans. Roy. Soc. 357, 2009-2133, 1999 (with J.N. Dewynne & P. Wilmott).
1. Some aspects of the Stefan model for phase changes, in Proceedings of the NATO Symposium on Structure and Dynamics of Partially Solidified Systems, ed. D.E. Loper, Nijhoff 1987.
2. Equilibrium distributions of screw dislocations, in Proceedings of the Conference on Free Boundary Problems, Irsee 1987, ed. K.-H. Hoffman, Longman 1989.
3. Some remarks concerning the mathematical theory of solidification, in Proceedings of Solidification Processing 1987, 370-372, Institute of Metals (London) 1988 (with A.B. Crowley & J.R. Ockendon).
4. Temperature surges in thermistors, in Proceedings of the Third European Symposium on Mathematics in Industry, ed. J. Manley, 197-204, Teubner 1990 (with A.C. Fowler).
5. Kinetic undercooling regularisation of supercooled Stefan Problems, in Mathematical Models for Phase Change Problems, ed. J-F Rodrigues, Birkhauser 1989 (with W. Xie).
6. On the singularities of one-dimensional Stefan problems with supercooling, in Mathematical Models for Phase Change Problems, ed. J-F Rodrigues,Birkhauser 1989 (with A. Fasano, M. Primicerio & J.R. Ockendon).
7. The numerical solution of a continuous casting problem, in Free Boundary problems, eds K.-H. Hoffmann & J. Sprekels, International Series of Numerical Mathematics 95, Birkhauser-Verlag Basel 1990 (with J.N. Dewynne & J.R. Ockendon).
8. Codimension-two free boundary problems, in Proc. Int'l. Coll. on Free Boundary Problems, ed J. Chadam & H. Rasmussen, Pitman 1991 (Plenary lecture}.
9. Black-Scholes models for financial derivative products, in Proc. ECMI Conference on Mathematics in industry, ed. A. Fasano, Teubner, 1995 (with J.N. Dewynne).
10. Patch cavitation in flow past a rigid body, in Proceedings of the IUTAM Workshop on Cavitated Flows, Birmingham 1993, ed. J.R. Blake (with J.D. Morgan & J.R. Ockendon).
11. Trading volume in models of financial derivatives, in proceedings ECMI Conference (2000), ed. V. Capasso, Springer 2001 (with David Lamper.)
12. Vortex velocity laws to I-V data for flat superconductors, IEEE Trans. Appl. Superconductivity 11, 3943-3946, 2001 (with S.J. Chapman, A.D. Grief, M.D. McCulloch, D. Dew-Hughes, J. Moore & C.M. Grovenor).
13. P. Ya Kochina i Khele-Shou v sovremennoi matematike, estestvennykh naukakh i tekhnike, Prikl. Mat. Mech., 2002 (with J.R. Ockendon, transl. V.M. Entov) (Plenary lecture). PDF version in Russian
14. A note on the pricing and hedging of volatility derivatives, Bachelier Finance Society Proceedings 2002, with A. Rafailidis & H.O. Rasmussen.
15. Monte-Carlo techniques for American options, in Progress in Industrial Mathematics, Proc. ECMI conference 2002, Ed. A Buikis et al., Springer 2004 (with D. Lamper). (PDF here.)
16. What shakes the FX tree? Understanding currency dominance, dependency and dynamics. Proc. SPIE conference on fluctuations and noise, 2005 (with M. McDonald, N.F. Johnson,O. Suleman and S. Williams).