Research interests
- Lévy processes.
- Stochastic control problems.
- Insurance mathematics.
- Financial mathematics.
If you are interested in doing a PhD under my supervision in the areas mentioned above, then feel free to contact me about this.
Publications
- Lévy processes in finance distinguished by their coarse and fine path properties.
With A.E.
Kyprianou.
Exotic option pricing and advanced Lévy models, eds.
A. Kyprianou, W. Schoutens and P. Wilmott. Wiley, 2005.
- On optimality of the barrier strategy in de Finetti's dividend problem for
spectrally negative Lévy processes.
Annals of Applied Probability
2008, Vol. 18, No. 5, 1669-1680.
- Refracted
Lévy processes.
With A.E.
Kyprianou.
Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
2010, Vol. 46, No. 1, 24-44 .
- An
optimal dividends problem with a terminal value for spectrally negative
Lévy processes with a completely monotone jump density.
Journal of Applied Probability
2009, Vol. 46, No. 1, 85-98.
- An optimal dividends problem with transaction costs for spectrally negative
Lévy processes.
Insurance:
Mathematics and Economics 2009, Vol. 45, No. 1, 41-48.
- De Finetti's optimal dividends problem with an affine penalty function
at ruin.
With J.-F. Renaud.
Insurance:
Mathematics and Economics 2010, Vol. 46, No. 1, 98-108 (Special
Issue on Gerber-Shiu Functions).
- Optimal control with absolutely continuous strategies for spectrally negative Lévy processes.
With A.E.
Kyprianou and J.-L. Pérez.
Journal of Applied Probability
2012, Vol. 49, No. 1, 150-166.
- Parisian ruin probability for spectrally negative Lévy processes.
With I. Czarna
and Z. Palmowski.
Bernoulli
2013, Vol. 19, No. 2, 599-609.
- Semi-Closed Form Cubature and Applications to Financial Diffusion Models.
With C. Bayer
and P. Friz.
Quantitative Finance
2013, Vol. 13, No. 5, 769-782.
- Occupation times of intervals until first passage times for spectrally negative Lévy processes.
With J.-F. Renaud and
X. Zhou.
Stochastic Processes and their Applications
2014, Vol. 124, No. 3, 1408-1435.
- Smoothness of continuous state branching with immigration semigroups.
With M. Chazal and P. Patie.
Journal of Mathematical Analysis and Applications
2018, Vol. 459, Issue 2, 619-660.
- Option pricing in a one-dimensional affine term structure model via spectral representations.
With M. Chazal and P. Patie.
SIAM Journal on Financial Mathematics
2018, Vol. 9, Issue 2, 634-664.
- Discounted Penalty Function at Parisian Ruin for Lévy Insurance Risk Process.
With Z. Palmowski
and B. Surya.
Insurance: Mathematics and Economics
2018, Vol. 83, 190-197.
- Extinction time of non-Markovian self-similar processes, persistence, annihilation of jumps and the Fréchet distribution.
With P. Patie and M. Savov.
Journal of Statistical Physics
2019, Vol. 175, Issue 5, 1022-1041.
- On obtaining simple identities for overshoots of spectrally negative Lévy processes.
Submitted.
- The equivalence of two tax processes.
With D. Al Ghanim and A.R. Watson.
Insurance Mathematics and Economics
2020, Vol. 90, 1-6.
- First passage times over stochastic boundaries for subdiffusive processes.
With C. Constantinescu and P. Patie.
Transactions of the American Mathematical Society 2022, Vol. 375, Number 3, 1629-1652.
- Optimal switching between two spectrally negative Lévy processes to minimise ruin probability.
With J. E. Martínez Sosa and K. van Schaik.
Submitted.
- Fluctuation theory of continuous-time skip-free downward Markov chains with applications to branching processes with immigration.
With P. Patie and J. Wang.
Submitted.