SD Howison, publications


1: Books 

1. Option Pricing: Mathematical Models and Computation (with JN Dewynne & P Wilmott). Oxford Financial Press 1993.


2. Mathematical Models in Finance (edited with FP Kelly and P Wilmott). Chapman & Hall 1995.


3. Mathematical Models of Financial Derivatives: a Student Introduction (with P Wilmott & JN Dewynne). Cambridge University Press 1995.


4. Applied Partial Differential Equations (with JR Ockendon, AA Lacey & AB Movchan). Oxford University Press 1999 (revised edition 2003).


5. Practical Applied Mathematics: Modelling, Analysis, Approximation, Cambridge University Press, 2005.


2: Refereed papers

80. The long memory of order flow in the foreign exchange spot market, Market Microstructure and Liquidity 2(1), 1650001, 2016 (with MD Gould and MA Porter). Author-accepted version from ORA.

79.  Quasi-centralized limit order books, 2015 preprint on (with MD Gould & MA Porter).

78, Community detection in temporal multilayer networks, and its application to correlation networks,
Multiscale Modelling & Simulation 14(1), 1-41, 2016 (with M Bazzi, MA Porter, S Williams, M McDonald & DJ Fenn), published version here.

77. Risk-Neutral Pricing of Financial Instruments in Emission Markets: A Structural Approach
, SIAM Review 57, 95-127, 2015 (with D Schwarz), available here.

76. Limit Order Books, Quantitative Finance 13, 1709-1742, 2013 (with D Fenn, M Gould, M MacDonald, MA Porter & S Williams), available here.

75. The Effect of Non-Smooth Payoffs on the Penalty Approximation of American Options, SIAM J. Financial Mathematics 4, 539-574, 2013 (with Christoph Reisinger and Jan Hendrik Witte), available here.

74. Three-dimensional oblique  water entry problems at small deadrise angle, J. Fluid Mech 711 259-280, 2012 (with JR Ockendon, MR Moore & JM Oliver), (PDF here.

73. A note on oblique water entry, now online, J. Eng. Math. 2012 (with JR Ockendon, MR Moore & JM Oliver), PDF here.

72. Partial Differential Equations that are hard to classify. J. Part. Diff. Eq. 25, 41-65, 2012 (with AA Lacey & JR Ockendon). pdf here

71.Risk-Neutral Pricing of Financial Instruments in Emission Markets: A Structural Approach, SIAM J. Financial Math. 3, 709-739, 2012 (with D Schwarz), available here.

70. Asymptotic approximations for Asian, European and American options with discrete averaging, or discrete dividend/coupon payments. SIAM J. Financial Math. 3, 215-241, 2012, PDF here.

69. Games with exhaustible resources,  SIAM J. Appl. Math. 70, 2556-2581,  2010 (with Chris Harris & Ronnie Sircar). PDF of a slightly extended version of the paper is available here.

68. Modelling spikes and pricing swing options in electricity markets, Quantitative Finance 9, 937-949, 2009 (with B Hambly & T Kluge), PDF here.

67. Option pricing with Levy-stable processes generated by Levy-stable integrated variance.  Quantitative Finance 9,  397-409, 2009 (with A Cartea), PDF here.

66. Stochastic behavior of the electricity bid stack: from fundamental drivers to power prices. J. Energy Markets 2(1), 2009 (with M Coulon), PDF 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 & NF Johnson), PDF here.

64. Impact of unexpected events, shocking news, and rumors on foreign exchange market dynamics. Phys. Rev. E 77, 46110-46122, 2008 (with M McDonald, O Suleman, S Williams & NF Johnson).

63. Non-classical shallow water flows. I.M.A. J. Appl. Math. 73, 137-157, 2008 (with Carina Edwards, H Ockendon & JR Ockendon), PDF here.)

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 CL 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 & JR 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 & NF Johnson).


57. Droplet impact on a thin fluid layer, J. Fluid. Mech. 542, 1-23, 2005 (with JR Ockendon, JM Oliver, R Purvis & FT 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 JA Addison &  JR King). PDF here.

54. A comparison of option prices under different pricing measures in a stochastic volatility model with correlation,  Rev. Deriv. Research 8, 5-25, 2005 (with V Henderson, D Hobson & T Kluge). 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 JM 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 MJ Siegel & RE 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 AA Lacey & JR Ockendon). PDF here.

48. Oblique slamming, planning and skimming, J. Eng. Math. 48, 321-337, 2004 (with JM Oliver & JR Ockendon). PDF here.

47. Deep- and shallow-water slamming at small and zero deadrise angles, J. Eng. Math. 42, 373-388, 2002  (with JM Oliver & JR Ockendon). PDF here.

46. Application of multi-agent games to the prediction of financial time series, Physica A 299, 222-227, 2001 (with NF Johnson, D Lamper, P Jefferies & ML Hart).

45. Predictability of large future changes in a competitively evolving population, Phys. Rev. Lett. 88 017902, 2002 (with NF 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 LJ Cummings). PDF here.

41. Two-dimensional Stokes and Hele-Shaw flow with free surfaces, Europ. J. Appl. Math. 10, 635-680, 1999 (with LJ Cummings & JR King).  PDF here.

40. Two-dimensional solidification  and melting in Darcy flow,  J. Fluid Mech. 378, 1-18, 1999 (with L.J. Cummings, YuE Hohlov & K Kornev). PDF here.


39. Computation of deterministic volatility surfaces, J. Comp. Finance 2, 5-32, 1999 (with E Suli & NA Jackson).

38. Dynamics of line singularities, Phil. Trans. Roy. Soc. 355, 2013-2024, 1997 (with A Carpio, SJ Chapman & JR Ockendon).

37. Numerical and asymptotic solution of a sixth-order nonlinear diffusion equation and related coupled systems, IMA J. Appl. Math. 57, 79-98, 1996 (with WR Smith & DF Mayers).

36. A mathematical model for drying paint layers, J. Eng. Math. 32, 377-394, 1997 (with J Moriarty, JR Ockendon, L Terrill & SK Wilson).

35. Conserved quantities in Stokes flow with free surfaces, Phys. Fluids  9, 477-480, 1997 (with LJ Cummings & JR King).


34. Asymptotics of violent surface motion, Phil. Trans. Roy. Soc. 355, 679-685, 1997  (with SJ Chapman, KA Gillow & JR Ockendon).


33. A class of codimension two free boundary problems, SIAM Review 39, 221-253, 1997 (with JD Morgan & JR Ockendon).


32. A dynamic simulation of the conforming shell gas journal bearing, J. Eng. Math. 29, 557-574, 1995 (with DF Mayers & WR Smith).


31. Cusp development in free boundaries and two-dimensional slow viscous flows, Europ. J. Appl. Math. 6, 441-454, 1995 (with S  Richardson).


30. Applied mathematics and finance, Phil. Trans Roy. Soc. A347, 465-470, 1994.


29. On the stability of Poiseuille flow of a Bingham Fluid, J. Fluid Mech. 263, 133-150, 1994 (with I Frigaard and I Sobey).


28. An equilibrium theory of dislocation continua, SIAM Review  35, 580-609, 1993 (with AK Head. JR Ockendon & SP Tighe).


27. Some mathematical results in the pricing of American Options, Europ. J. Appl. Math. 4, 381-398, 1993 (with JN 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, AA Lacey & JR 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 RJ 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 SJ Chapman & JR Ockendon).

21. Mathematical modelling of dislocation plasticity, Physica Scripta T44, 135-136, 1992 (with AK Head, JR Ockendon & SP 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 SJ Chapman, JB McLeod & JR 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 AA Lacey, JR Ockendon & P Wilmott).

16. Inviscid water entry problems at small deadrise angles, J. Fluid Mech. 222, 215-230, 1991 (with JR Ockendon & SK Wilson).

15. Temperature surges in current-limiting circuit devices, SIAM J. Appl. Math. 52, 998-1011, 1992 (with AC 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 & JR Ockendon).

13. A note on the thermistor problem in two space dimensions, Q. Appl. Maths 47, 509-512, 1989.

12. Asymptotic behaviour of solutions to the Stefan problem with a kinetic condition at the free boundary, J. Aust. Math. Soc. Ser. B, 31, 81-96, 1989 (with JN Dewynne, JR Ockendon & W Xie).

11. Explicit solutions to six free boundary problems in fluid flow and diffusion, IMA J. Appl. Maths 42, 155-175, 1989 (with JR King).

10. Similarity solutions to the Stefan problem and the binary alloy problem, IMA J. Appl. Maths 40, 147-161, 1988.

9. Slot suction from inviscid channel flow, J. Fluid Mech. 200, 265-282, 1989 (with JN Dewynne, LC Morland, JR Ockendon & EJ Watson).


8. Hele-Shaw free boundary problems with suction, Q. J. Mech. Appl. Maths  41, 183-193, 1988 (with AA Lacey & JR Ockendon).

7. Existence and stability for spherical crystals growing in a supersaturated solution, IMA 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  AK Head, JR Ockendon, JB 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.

3. Cusp development in Hele-Shaw flow with a free surface, SIAM J. Appl. Math. 46, 20-26, 1986.

2. Singularity development in moving boundary problems, Quart. J. Mech. Appl. Maths 38, 343-360, 1985 (with AA Lacey & JR Ockendon).

1. Numerical computation of Hele-Shaw flows with free boundaries, J. Comp. Phys.  36, 376-390, 1985 (with JM Aitchison).

3: Edited  collections


1. Mathematical Models in Finance, proceedings of a Royal Society Discussion Meeting, Phil. Trans. Roy. Soc. 347, 449-598, 1994 (with FP Kelly FRS & P Wilmott).


2. Violent Surface Motion, proceedings of a Royal Society Discussion Meeting, Phil. Trans. Roy. Soc. 355, 487-689, 1997 (with JR Ockendon FRS, DH Peregrine & DW 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 SJ Chapman, CM Elliott, AK Head FRS, FM Leslie, & JR Ockendon FRS).


4. Mathematics in Finance, themed issue of Phil. Trans. Roy. Soc. 357, 2009-2133, 1999 (with JN Dewynne  & P Wilmott).

4: Plenary lectures and refereed conference proceedings


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. DE 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 AB Crowley & JR 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 AC 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 & JR 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 JN  Dewynne & JR 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 JN Dewynne).


10. Patch cavitation in flow past a rigid body, in Proceedings of the IUTAM Workshop on Cavitated Flows, Birmingham 1993, ed. JR Blake (with JD Morgan & JR 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 SJ Chapman, AD Grief, MD McCulloch, D Dew-Hughes, J Moore & CM Grovenor).


13. P Ya Kochina i Khele-Shou v sovremennoi matematike, estestvennykh naukakh i tekhnike, Prikl. Mat. Mech., 2002 (with JR Ockendon, transl.  VM Entov) (Plenary lecture).  PDF version in Russian

and English.

14. A note on the pricing and hedging of volatility derivatives, Bachelier Finance Society Proceedings 2002, with A Rafailidis & HO 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, NF Johnson,O Suleman and S Williams).