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A. E. Kyprianou: research

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I collaborate or have had collaboration with the following people:

Larbi Alili, Florin Avram, Laura Ballotta, Enrico Biffis, John Biggins, Erik Baurdoux, Julien Berestycki, Terence Chan, Loic Chaumont, Ron Doney, Hans Duistermaat, Nathalie Eisenbaum, Janos Englander, Ben Hambly, John Harris, Simon Harris, Friedrich Hubalek, Goetz Kersting, Takis Konstantopoulos, Claudia Kluppelberg, Robert Knobloch, Christoph Kuhn, Alexey Kuznetsov, Ronnie Loeffen, Rongli Liu, Ross Maller, Antonio Murillo, Zbigniew Palmowski, Pierre Patie, Martijn Pistorius, Juan Carlos Pardo, Yanxia Ren, VIctor Rivero, Paavo Salminen, Mladen Savov, Ali Akbar Rahimzadeh Sani, Kees van Schaik, Wim Schoutens, Marina Sirvio (née Kozlova), Renming Song, Budhi Arta Surya, Matthias Winkel, Vladimir Vatutin, Xiaowen Zhou.

I have supervised or am supervising the following Ph.D. students:

I was or am the grant holder/scientific supervisor of the following postdocs:

I have hosted or am hosting the following visiting research fellows thanks to the EPSRC small grant scheme for mathematics or the Royal Society International Incoming Short Visits:

*joint grant with Simon Harris.

I serve on the editorial boards of the following journals:

I am also a member of the EPSRC peer review college (2006-present)

Theses and books

Published or appearing

  1. Branching Random Walk: Seneta-Heyde norming. (with J.D. Biggins)
    In Trees (B.Chauvin, S. Cohen, and A. Rouault, eds) Birkhaser, Basel, 1995.
  2. Seneta-Heyde norming in the branching random walk. (with J.D. Biggins).
    Annals of Probabability (1997) 25, 337-360.
  3. Slow variation and uniqueness of solutions to the functional equation in the branching random walk.
    Journal of Applied Probability (1998) 35, 795-802.
  4. A note on branching Lévy processes.
    Stochastic Processes and their Applications (1999) 82, 1-14.
  5. Martingale Convergence and the Stopped Branching Random Walk.
    Probability Theory and Related Fields (2000) 116, 405--419.
  6. Martingale convergence and the functional equation in the multi-type branching random walk. (with A. Rahimzadeh Sani).
    Bernoulli. (2001) 7(4), 593--604.
  7. A note on the alpha-quantile option. (with Laura Ballotta).
    Applied Mathematical Finance (2001) 8, 137--144
  8. Perpetual options and Canadization through fluctuation theory. (with Martijn Pistorius).
    Annals of Applied Probability (2003) 13(3), 1077-1098.
  9. Law of the iterated logarithm for oscillating random walks conditioned to stay non-negative. (with B. Hambly and G.Kersting)
    Stochastic Processes and their Applications (2003) Vol 108/2 pp 327-343.
  10. Some calculations for Israeli options.
    Finance and Stochastics. (2004) 8, 73 - 86.
  11. Local extinction versus local exponential growth for spatial branching processes. (with Janos Englander)
    Annals of Probability (2004) 32, 78-99.
  12. Exit problems for spectrally negative Lévy processes adn applications to (Canadized) Russian options. (with F.Avram and Martijn Pistorius).
    Annals of Applied Probability (2004) 14(1), 215-238.
  13. Travelling wave solutions to the K-P-P equation: alternitives to Simon Harris' probabilistic analysis.
    Annales de l'Instut Henri Poincaré. (2004) 40(1), 53-72.
  14. Ruin probabilties and overshoots for general Lévy insurance risk process. (with C. Kluppelberg and Ross Maller).
    Annals of Applied Probability (2004) 14(4), 1766-1801.
  15. Measure change in multitype branching. (with J.D. Biggins).
    Advances in Applied Probability (2004) 36(2) 544-581.
  16. A martingale review of some fluctuation theory for spectrally negative Lévy processes. (with Z. Palmowski).
    Séminaire de Probabilité XXXVIII, 16-29.
  17. Further calculations for Israeli options. (with Erik Baurdoux).
    Stochastics (2004) 76, 549-569.
  18. Asymptotic radial speed of the support of supercritical branching and super-Brownian motion in R^d.
    Markov Processes and Related Fields. (2005) 11, 145-156.
  19. Finite expiry Russian options. (with Kees van Schaik and Hans Duistermaat).
    Stochastic Processes and their Applications. (2005) Vol 115/4, 609-638.
  20. Lévy processes in finance distinguished by their coarse and fine path properties. (with Ronnie Loeffen).
    In Exotic option pricing and advanced Lévy models Eds. A. Kyprianou, W. Schoutens and P. Wilmott. Wiley, 2005.
  21. The smoothing transform: the boundary case. (with J.D. Biggins).
    Electronic Journal of Probability (2005) 10, 609-631.
  22. Some remarks on first passage of Lévy process, the American put and pasting principles. (with Larbi Alili).
    Annals of Applied Probability (2005) 15, 2062--2080.
  23. On the Novikov-Shiryaev optimal stopping problem in continuous time. (with B. Surya).
    Electronic Communications in Probability (2005) 10, 146-154.
  24. Further probabilistic analysis of the Fisher-Kolmogorov-Petrovskii-Piscounov equation: one sided travelling waves. (with John Harris and S. C. Harris).
    Annales de l'Instut Henri Poincaré (2006), 42, 125-145.
  25. Overshoots and Undershoots of Lévy process (with Ron Doney).
    Annals of Applied Probability (2006) 16, 91-106.
  26. First passage of reflected strictly stable processes.
    ALEA (2006) 2, 119-123.
  27. On extreme ruinous behaviour of Lévy insurance risk processes. (with C. Kluppelberg).
    Journal of Applied Probability (2006) 43, 594-598.
  28. Quasi-stationary distributions for Lévy process. (with Z. Palmowski).
    Bernoulli (2006) 12, 571-581.
  29. Principles of smooth and continuous fit in the determination of endogenous bankruptcy levels. (with B. Surya).
    Finance and Stochastics (2007) 11, 131-152.
  30. Pricing Isreali options: a pathwise approach. (with C. Kuhn and K. van Schaik).
    Stochastics (2007) 79, 117-137.
  31. Distributional study of De Finetti's dividend problem for a general Lévy insurance risk process. (with Z. Palmowski)
    Journal of Applied Probability. (2007) 44, 428-443.
  32. A note on the change of variable formula with local time-space for bounded variation Lévy processes. (With B. Surya).
    Séminaire de Probabilité XL. 97-105.
  33. Callable puts as composite exotic options. (with C. Kuhn).
    Mathematical Finance (2007) 17, 487-502.
  34. The McKean stochastic game driven by a spectrally negative Lévy process. (with Erik Baurdoux).
    Electronic Journal of Probability. (2008) Paper no. 8, 173-197.
  35. Fluctuations of spectrally negative Markov Additive Processes. (with Z. Palmowski).
    Séminaire de Probabilité XLI. 121-135.
  36. On the parabolic generator of a general one-dimensional Lévy process. (with Nathalie Eisenbaum).
    Electronic Communications in Probability (2008) Paper no. 20, 198-209.
  37. Special, conjugate and complete scale functions for spectrally negative Lévy processes. (with V. Rivero).
    Electronic Journal of Probability (2008) Paper no 57, 1672-1701.
  38. Continuous state branching processes and self-similarity. (with Juan Carlos Pardo).
    Journal of Applied Probability (2008) 45 (4), 1140-1160.
  39. Analysis of stochastic fluid queues driven by local time processes. (with Takis Konstantopoulos, Paavo Salminen and Marina Sirvio (née Kozlova)).
    Advances of Applied Probability (2008) vol. 40 (4), 1072-1103.
  40. Branching processes in random environment die slowly. (with V.Vatutin).
    Discrete Mathematics & Theoretical Computer Science Proceedings Fifth Colloquium on Mathematics and Computer Science (2008) 375-396.
  41. Some explicit identities associated with positive self-similar Markov processes. (with Loic Chaumont and Juan Carlos Pardo).
    Stochastic Processes and Their Applications (2009) 119/3, 980-1000
  42. The Shepp-Shiryaev stochastic game driven by a spectrally negative Lévy process. (with Erik Baurdoux).
    Theory of Probability and Its Applications (Teoriya Veroyatnostei i ee Primeneniya) (2009) 53, 481-499.
  43. General tax structures and the Lévy insurance risk model. (with Xiaowen Zhou).
    Journal of Applied Probability (2009) 46, 1146-1156.
  44. A note on scale functions and the time value of ruin for Lévy insurance risk processes. (with Enrico Biffis).
    Insurance Mathematics and Economics (2010) 46, 85-91.
  45. Refracted Lévy processes. (with R. Loeffen).
    Annales de l'Instut Henri Poincaré (2010), 46, 24-44..
  46. Strong law of large numbers for fragmentation processes. (with S.C. Harris and R.Knobloch).
    Annales de l'Instut Henri Poincaré (2010) 46, 119-134.
  47. Strong law of large numbers for branching diffusions. (with Janos Englander and Simon Harris).
    Annales de l'Instut Henri Poincaré (2010), 46, 279-298..
  48. The Wiener-Hopf decomposition.
    Encyclopedia of Quantitative Finance, published by Wiley.
  49. Lévy processes.
    Encyclopedia of Quantitative Finance, published by Wiley.
  50. Exact and asymptotic n-tuple laws at first and last passage. (with V. Rivero and Juan Carlos Pardo).
    Annals of Applied Probability (2010), Vol. 20, No. 2, 522-564.
  51. Convexity and smoothness of scale functions and de Finetti's control problem. (with V. Rivero and Renming Song).
    Journal of Theoretical Probability (2010) 23, 547-564.
  52. Old and new examples of scale functions for spectrally negative Lévy processes. (with F. Hubalek).
    Sixth Seminar on Stochastic Analysis, Random Fields and Applications, eds R. Dalang, M. Dozzi, F. Russo. Progress in Probability, Birkhäuser (2010) 119-146.
  53. The Gapeev--Kühn stochastic game driven by a spectrally positive Lévy process. (with Erik Baurdoux and Juan Carlos Pardo).
    Stochastic Processes and their Applications (2011) 121/6, 1266-1289.
  54. The prolific backbone for supercritical superdiffusions. (with Julien Berestycki and Antonio Murillo).
    Stochastic Processes and their Applications (2011) 121/6, 1315-1331.
  55. A Ciesielski-Taylor type identity for positive self-similar Markov processes (with Pierre Patie).
    Annales de l'Instut Henri Poincaré (2011) 47/3, 917-928.
  56. Smoothness of scale functions for spectrally negative Lévy processes (with Terence Chan and Mladen Savov).
    Probability Theory and Related Fields (2011) 150, 691-708
  57. On the excursions of reflected local time processes and stochastic fluid queues. (with Takis Konstantopoulos and Paavo Salminen).
    Journal of Applied Probability (2011), 48A, 79-98.
  58. Travelling waves and homogeneous fragmentation (with Julien Berestycki and Simon Harris).
    Annals of Applied Probability. (2011) 21, 1749-1794.
  59. A Wiener-Hopf Monte Carlo simulation technique for Lévy process (with Alexey Kuznetsov, Juan Carlos Pardo and Kees van Schaik).
    The Annals of Applied Probability. (2011) 21, 2171Ð2190
  60. Backbone decomposition for continuous-state branching processes with immigration. (with Yanxia Ren).
    Statistics and Probability Letters. (2012) 82, 139-144
  61. Fluctuation theory and exit systems for positive self-similar Markov processes (with Loic Chaumont, V. Rivero and Juan Carlos Pardo).
    Annals of Probability (2012) 40, 245-279
  62. Meromorphic Lévy processes and their fluctuation identities (with Alexey Kuznetsov, Juan Carlos Pardo).
    To appear in Annals of Applied Probability
  63. Supercritical super-Brownian motion with a general branching mechanism and travelling waves (with Antonio Murillo-Salas, Rongli Liu and Yanxia Ren).
    To appear in Annales de l'Instut Henri Poincaré.
  64. Optimal control with absolutely continuous strategies for spectrally negative Lévy processes. (with Ronnie Loeffen and Jose-Luis Pérez).
    To appear in the Journal of Applied Probability
  65. An optimal stopping problem for fragmentation processes. (with Juan Carlos Pardo).
    To appear in Stochastic Processes and their Applications.
  66. The theory of scale functions for spectrally negative Lévy processes. (with Alexey Kuznetsov and Victor Rivero).
    To appear in Lévy Matters, Springer Lecture Notes in Mathematics.
  67. An application of the backbone decomposition to supercritical super-Brownian motion with a barrier. (with Antonio Murillo-Salas and Jose-Luis Pérez).
    To appear in Journal of Applied Probability.

Submitted

  1. A transformation for Lévy processes with one-sided jumps and applications. (with Marie Chazal and Pierre Patie). This version 18.10.10.
  2. Super-Brownian motion: Lp-convergence of martingales through the pathwise spine decomposition. with Antonio Murillo-Salas). This version 31.04.11.
  3. Survival of homogenous fragmentation processes with killing. (with Robert Knobloch). This version 26.04.11.
  4. Efficient Pricing of Contingent Convertibles under Smile Conform Models. (with José Manuel Corcuera, Jan de Spiegeleer, Albert Ferreiro-Castilla, Dillip Madan and Wim Schoutens). This version 04.11.11.
  5. Hitting distributions of alpha-stable processes via path censoring and self-similarity (with Juan Carlos Pardo and Alex Watson). This version 15.12.11.

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