Pierre Patie
School of Operations Research and Information Engineering
Pierre Patie
Associate Professor
School of Operations Research
and Information Engineering
Cornell University

219 Rhodes Hall
Ithaca, NY 14853
(607) 255-9130 - phone
(607) 255-9129 - fax
pp396 "at" cornell.edu

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[Research interests] [Preprints/Publications]



Research interests

  • Spectral theory of non-self-adjoint semigroups and study of special functions

  • Exit times and additive functionals of Markov processes

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

  • Financial and insurance mathematics



Preprint

  1. Skip-free Markov chains, (with M.C.H. Choi)
    Submitted

  2. Spectral decomposition of fractional operators and reflected stable semigroups, (with Y. Zhao)
    Submitted

  3. Bernstein-gamma functions and exponential functionals of Lévy Processes (with M. Savov )
    Submitted

  4. Smoothness of continuous state branching with immigration semigroups, (with M. Chazal and R.L. Loeffen)
    Submitted

  5. Spectral expansions of non-self-adjoint generalized Laguerre semigroups (with M. Savov )
    Submitted

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

  7. Option pricing in a one-dimensional affine term structure model via spectral representations (with M. Chazal, and R.L. Loeffen)
    Submitted

  8. Publications

  9. Cauchy problem of the non-self-adjoint Gauss-Laguerre semigroups and uniform bounds of generalized Laguerre polynomials, (with M. Savov )
    J. Spectr. Theory, to appear, 2016.

  10. Boundary crossing identities for Brownian motion and some nonlinear ode's, (with L. Alili)
    Proc. Amer. Math. Soc. 142, 3811-3824, 2014.

  11. A transformation for Lévy processes with one-sided jumps with applications, (with M. Chazal and A.E. Kyprianou)
    Adv. Appl. Prob., to appear, 2014

  12. Exponential functionals of Lévy processes: generalized Weierstrass products and Wiener-Hopf factorization (with M. Savov )
    C. R. Math. Acad. Sci. Paris, 351, no. 9-10, 393-396., 2013

  13. Asion options under one-sided  Lévy models,
    J. of Appl. Prob. 50(2), 359-373, 2013

  14. Extended factorizations of exponential functionals of Lévy processes, (with M. Savov )
    Electron. J. Probab., 17(38): 1-22, 2012

  15. Law of the absorption time of positive self-similar Markov processes,
    Ann. Probab., 40(2): 765-787, 2012

  16. A Wiener-Hopf type factorization for the exponential functional of Lévy processes, (with J.-C. Pardo and M. Savov )
    J. London Math. Soc., 86(3): 930-956, 2012

  17. Optimal stopping problems for some Markov processes, (with M. Cissé and E. Tanré)
    Ann. Appl. Probab., 22(3): 1243–1265, 2012

  18. Intertwining certain fractional operators, (with T. Simon)
    Potent. Anal., 36: 569-587, 2012

  19. 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

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

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

  22. 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

  23. 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

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

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

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

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

  28. 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

  29. 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

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

  31. 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

  32. 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

  33. 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

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

  35. 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


  36. Proceedings

  37. Sufficient conditions for continuous time finite skip-free Markov chains to have real eigenvalues (with M.C.H. Choi )
    Mathematical and Computational Approaches in Advancing Modern Science and Engineering, to appear, 2016

  38. Convergence analysis of the spectral expansion of stable related semigroups (with Y. Zhao )
    Mathematical and Computational Approaches in Advancing Modern Science and Engineering, to appear, 2016






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