A. E. Kyprianou: research

Collaborators

Past/current Ph.D. students

• Martijn Pistorius (1999-2003) [Ph.D. thesis in PDF format] "Exit problems of Lévy processes with applications in finance".
• Budhi Arta Surya (2003-2007) [Ph.D. thesis in PDF format] "Optimal stopping problems driven by Lévy processes and pasting principles ".
• Erik Baurdoux (2003-2007) [Ph.D. thesis in PDF format] "Fluctuation Theory and Stochastic Games for Spectrally Negative Lévy Processes".
• Ronnie Loeffen (2005-2008) [Ph.D. thesis in PDF format] "Stochastic control for spectrally negative Lévy processes ".
• Robert Knobloch (2007-2010) [Ph.D. thesis in PDF format] "Asymptotic properties of fragmentation processes".
• Curdin Ott (2010-2013) [Ph.D. thesis in PDF format] "Optimal Stopping Problems for the Maximum Process".
• Alex Watson (2010-2013) [Ph.D. thesis in PDF format] "Stable processes".
• Marion Hesse (2010-2013) [Ph.D. thesis in PDF format] "Branching diffusions on the boundary and the interior of balls".
• Maren Eckhoff (2011-2014) [Ph.D. thesis in PDF format] "Superprocesses and Large-Scale Networks".
• Sandra Calderon (2012-2016)** [Ph.D. thesis in PDF format] "Generalisations of Continuous State Branching Processes"
• Stephen Pagett (2013-2016) "Fragmentation and Coalescence Processes: Theory and Applications"
• Francis Lane (2013-2017)
• Weerapat (Pite) Satitkanitku (2015-2018)***
• Dorottya Fekete (2015-2018)
• Emma Horton (2016-2020)

***Bath-CIMAT co-supervision in Bath, with V. Rivero

Past/current postdocs (with funding source)

• Z. Palmowski (2004-2005) and (2006-2007) [Funded by NWO - The Netherlands]
• Peter Andrew (2004-2006) [Funded by NWO - The Netherlands]
• Juan Carlos Pardo (2007-2009) [Funded by EPSRC - UK]
• Kees van Schaik (2009-2010) [Funded by AXA Research Fund]
• Antonio Murillo-Salas (2009-2011) [Funded by CONACyT]
• Élie Aidekon (2009) [Visiting from École Normale Supérieure]
• Jose Luis Garmendia Pérez (2010-2012) [Funded by CONACyT]
• Albert Ferreiro-Castilla (2012-2014) [Funded by a Royal Society Newton International Fellowship]
• Bati Sengul (2014-2016) [Funded by EPSRC - UK]

Past/current visiting researchers (with funding source)

• Prof. Vladimir Vatutin (Steklov Institute, Russia) [May-June 2006: EPSRC] Click here for his lectures.
• Prof. Janos Englander (Santa Barbara, USA)* [July-August 2007: EPSRC] Click here for more on his lectures and activities around his visit.
• Prof. Goetz Kersting (Frankfurt, Germany)* [July 2007: EPSRC] Click here for more on his lecture and activities around his visit.
• Prof. Renming Song (Illinois, USA) [December 2007: EPSRC]
• Prof. Victor Rivero (CIMAT, Mexico) [April - June 2008: Royal Society]
• Prof. Julien Berestycki (Paris VI) [March - September 2009: Royal Society and BICS]
• Prof. Victor Rivero (CIMAT, Mexico) [Oct 2014 - Sept 2015: EPSRC]

*joint grant with Simon Harris.

Journal editorial

• Advances in Applied Probability,
• Journal of Applied Probability,
• Stochastics: An International Journal of Probability and Stochastic Processes.
• Acta Applicandae Mathematicae.
• ALEA: Latin American Journal of Probability and Mathematical Statistics.

Book series editorial

• Springer: Stochastic Modelling and Applied Probability.
• Birkhäuser: Probability and its Applications.
• Birkhäuser: Progress in Probability.

EPSRC

Books: published or appearing

• Exotic option pricing and advanced Lévy models. (Eds. A. Kyprianou, W. Schoutens and P. Wilmott.) Wiley, 2005.
• Introductory Lectures on fluctuations of Lévy process with applications. Universitext, Springer, 2006.
• The theory of scale functions for spectrally negative Lévy processes. (with Alexey Kuznetsov and Victor Rivero).
  Lévy Matters II, Springer Lecture Notes in Mathematics, 2013.
• Fluctuations of Lévy process with applications (Second edition). Universitext, Springer, 2013.
• Gerber-Shiu Risk Theory. EAA Series, Springer, 2013.

Journals: 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).
    Annals of Applied Probability. (2011) 21, 2171-2190.
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. Optimal control with absolutely continuous strategies for spectrally negative Lévy processes. (with Ronnie Loeffen and Jose-Luis Pérez).
    Journal of Applied Probability (2012) 49, 150-166.
63. An optimal stopping problem for fragmentation processes. (with Juan Carlos Pardo).
    Stochastic Processes and their Applications. (2012) 122, 1210-1225.
64. Meromorphic Lévy processes and their fluctuation identities (with Alexey Kuznetsov, Juan Carlos Pardo).
    Annals of Applied Probability. (2012) 22, 1101-1135.
65. Supercritical super-Brownian motion with a general branching mechanism and travelling waves (with Antonio Murillo-Salas, Rongli Liu and Yanxia Ren).
    Annales de l'Instut Henri Poincaré. (2012) 48, 661-687.
66. Super-Brownian motion: Lp-convergence of martingales through the pathwise spine decomposition. (with Antonio Murillo-Salas).
    In Advances in Superprocesses and Nonlinear PDEs Series: Springer Proceedings in Mathematics & Statistics, Vol. 38 Englander, Janos; Rider, Brian C. (Eds.), 2013.
67. An application of the backbone decomposition to supercritical super-Brownian motion with a barrier. (with Antonio Murillo-Salas and Jose-Luis Pérez).
    Journal of Applied Probability. (2012) 49, 671-684.
68. Spectrally negative Lévy processes perturbed by functionals of their running supremum (with Curdin Ott).
    Journal of Applied Probability (2012) 49, 1005-1014.
69. On optimal dividends in the dual model (with Erhan Bayraktar and Kazutoshi Yamazaki).
    ASTIN Bulletin (2013) 43, 359-372.
70. Pricing of Contingent Convertibles under Smile Conform Models. (with José Manuel Corcuera, Jan de Spiegeleer, Albert Ferreiro-Castilla, Dillip Madan and Wim Schoutens).
    Journal of Credit Risk (2013) 9(3), 121-140.
71. Multilevel Monte Carlo simulation for Lévy processes based on the Wiener-Hopf factorisation (with Albert Ferreiro-Castilla, Rob Scheichl and Gowri Suryanarayana).
    Stochastic Processes and its Applications (2014) 124, 985-1010.
72. Optimal dividends in the dual model under transaction costs (with Erhan Bayraktar and Kazutoshi Yamazaki).
    Insurance: Mathematics and Economics (2014) 54, 133-143.
73. Hitting distributions of alpha-stable processes via path censoring and self-similarity (with Juan Carlos Pardo and Alex Watson).
    Annals of Probability. (2014) 42, 398-430
74. A capped optimal stopping problem for the maximum process (with Curdin Ott).
    Acta Applicandae Mathematicae. (2014) 129, 147-174
75. The total mass of super-Brownian motion upon exiting balls and Sheu's compact support condition. (with Marion Hesse).
    Stochastic Processes and its Applications (2014), 124, 2003-2022.
76. The hitting time of zero for a stable process (with Alexey Kuznetsov, Juan Carlos Pardo and Alex Watson).
    Electronic Journal of Probability (2014) 19, 1-26.
77. Survival of homogenous fragmentation processes with killing. (with Robert Knobloch).
    Annales de l'Instut Henri Poincaré (2014) 50, 476-491
78. New families of subordinators with explicit transition probability semigroup. (with James Burridge, Mateusz Kwasnicki, Alexey Kuznetsov.).
    Stochastic Processes and their Applications (2014) 124, 3480-3495
79. Occupation times of refracted Lévy processes (with Juan Carlos Pardo and Jose-Luis Pérez).
    Journal of Theoretical Probability. (2014) 27, 1292-1315.
80. The extended hypergeometric class of Lévy processes (with Juan Carlos Pardo and Alex Watson).
    Journal of Applied Probability. (2014) 51A, 391-408.
81. The backbone decomposition for spatially dependent supercritical superprocesses (with Jose-Luis Pérez and Yanxia Ren).
    To Séminaire de Probabilité XLVI. (2015) 33-60.
82. Potentials of stable processes (with Alex Watson).
    Séminaire de Probabilité XLVI. (2015) 333-344.
83. Spines, skeletons and the Strong Law of Large Numbers for superdiffusions (with Maren Eckhoff and Matthias Winkel).
    Annals of Probability. (2015), Vol. 43, No. 5, 2594-2659.
84. Branching Brownian motion in a strip: survival near criticality. (with Simon Harris and Marion Hesse).
    Annals of Probability. (2016) Vol. 44, No. 1, 235-275.
85. An Euler-Poisson Scheme for Lévy driven SDEs (with Albert Ferreiro-Castilla and Rob Scheichl).
    Journal of Applied Probability. (2016), 53, 262-278
86. UK universities find a cash cow in the financial fall-out
    The Conversation. (See also the longer version The UK financial mathematics M.Sc..)
87. Deep factorisation of the stable process.
    Electronic Journal of Probability. (2016), Volume 21 paper no. 23, 1-28..
88. More on hypergeometric Lévy processes (with Emma Horton).
    Advances in Applied Probability (2016) 48A, 153 - 158.
89. Optimal prediction for positive self-similar Markov processes (With Erik Baurdoux and Curdin Ott).
    Electronic Journal of Probability. (2016) Volume 21 paper no. 48, 1-24.
90. Perpetual integrals for Lévy processes (with Leif Doering).
    To appear in Journal of Theoretical Probability.
91. Real self-similar Markov processes started from the origin (with Steffen Deriech and Leif Doering).
    To appear in Annals of Probability.
92. Conditioned subordinators and applications.. (with VIctor Rivero, and Bati Sengul ).
    To appear in Stochastic Processes and their Applications.
93. A phase transition in excursions from infinity of the "fast" fragmentation-coalescence process. (with Steven Pagett, Tim Rogers and Jason Schweinsberg).
    To appear in Annals of Probability.
94. Deep factorisation of the stable process II: potentials and applications. (with Victor M. Rivero and Bati Sengul).
    To appear in Annales de l'Instut Henri Poincaré.

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. Universality in a class of fragmentation-coalescence processes.. (with Steven Pagett and Tim Rogers). This version 02.04.2015.
3. The Seneta-Heyde scaling for homogeneous fragmentations.. (with Thomas Madaule). This version 06.07.2015.
4. Conditioned real self-similar Markov processes.. (with Victor M. Rivero and Weerapat Satitkanitkul). This version 06.10.2015.
5. The largest fragment of a homogeneous fragmentation process (With Peter Mörters and Francis Lane).
6. Extinction properties of multi-type continuous-state branching processes (With Sandra Palau).
7. Stable windings at the origin. (With Stavros Vakeroudis).
8. Unbiased "walk-on-spheres" Monte Carlo methods for the fractional Laplacian (With Ana Osojnik and Tony Shardlow).

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