Pierre Patie

Research interests

• Fine properties of the Brownian motion, Lévy processes, self-similar processes and some generalizations of the Ornstein-Uhlenbeck process


• Law of exit times and additive functionals of Markov processes


• Special functions


• Financial mathematics: Exotic options and risk management

Submitted Papers

1. Extended factorizations of exponential functionals of Lévy processes, (with M. Savov)
   Submitted, 2011


2. A Wiener-Hopf type factorization for the exponential functional of Lévy processes, (with J.-C. Pardo and M. Savov)
   Submitted, 2011


3. A Geman-Yor formula for one-sided Lévy processes,
   Submitted, 2011


4. A transformation for Lévy processes with one-sided jumps with applications, (with M. Chazal and A.E. Kyprianou)
   Submitted, 2010


5. Absolute ruin in the Ornstein-Uhlenbeck type risk model, (with R.L. Loeffen)
   Submitted, 2010


6. Option pricing in stochastic volatility models of the CBI type, (with D. Burren)
   Submitted, 2009



Publications

7. Intertwining certain fractional operators, (with T. Simon)
   Potent. Anal., to appear, 2011


8. Optimal stopping problems for some Markov processes, (with M. Cissé and E. Tanré)
   Ann. Appl. Prob., to appear 2011


9. Law of the absorption time of positive self-similar Markov processes,
   Ann. Prob., to appear, 2010


10. A Ciesielski-Taylor type identity for positive self-similar Markov processes, (with A.E. Kyprianou)
    Ann. Inst. H. Poincaré Probab. Statist., 47(3):917–928, 2011


11. A refined factorization of the exponential law,
    Bernoulli, 17(2):814-826, 2011


12. Boundary crossing identities for diffusions having the time inversion property, (with L. Alili)
    J. Theoret. Probab., (23): 65–84, 2010


13. Exponential functional of a new family of Lévy processes and self-similar continuous state branching processes with immigration,
    Bull. Sci. Math., 133(4):355-382, 2009


14. Infinite divisibility of solutions to some self-similar integro-differential equations and exponential functionals of Lévy processes,
    Ann. Inst. H. Poincaré Probab. Statist., 45 (3):667--684, 2009


15. Law of the exponential functional of one-sided Lévy processes and Asian options,
    C. R. Acad. Sci. Paris, Ser. I ,347:407–411, 2009


16. A few remarks on the supremum of stable processes,
    Statist. Probab. Lett., 79:1125--1128, 2009


17. q-invariant functions for some generalizations of the Ornstein-Uhlenbeck semigroup,
    ALEA Lat. Am. J. Probab. Math. Stat.,4:31--43, 2008


18. First exit time probabilities for multidimensional diffusion: A PDE-based approach, (with C. Winter)
    J. Comput. Appl. Math., 222(1):43--53, 2008


19. On the joint law of the L¹ and L² norms of a 3-dimensional Bessel bridge, (with L. Alili)
    Séminaire de Probabilités XL:247-264, Lecture Notes in Math., 1899, Springer, Berlin, 2007


20. Two-sided exit problem for a spectrally negative α-stable Ornstein-Uhlenbeck process and the Wright's generalized hypergeometric functions,
    Elect. Com. Prob.,12:146-160, 2007


21. On a martingale associated to generalized Ornstein-Uhlenbeck processes and an application to finance,
    Stochastic Process. Appl., 115(4):593-607, 2005


22. Strategic Long-Term Financial Risks: The one dimensional case, (with P. Embrechts   and R. Kaufmann)
    Computational Optimization and Applications, 32(1-2):61-90,2005


23. Sur les premiers instants de croissement du mouvement brownien et d'une famille de courbes continues, (with L. Alili)
    C. R. Acad. Sci. Paris Sér. I Math., 340(3):225-228, 2005


24. Representations of the first hitting time density of an Ornstein-Uhlenbeck process, (with L. Alili  and J.L. Pedersen )
    Stochastic Models, 21(4):967-980, 2005


25. On some first passage times problems motivated by financial applications
    PhD Thesis, ETHZ, 2004.


26. Risk Management for Derivatives in Illiquid Markets: A Simulation Study, (with R. Frey)
    Advances in Finance and Stochastics, Klaus Sandmann and Philipp Schönbucher (Editors), 137--159, Springer, Berlin, 2002