On the Wiener–Hopf factorization for Lévy processes with bounded positive jumps
We study the Wiener–Hopf factorization for Lévy processes with bounded positive jumps and arbitrary negative jumps. We prove that the positive Wiener–Hopf factor can be expressed as an infinite product involving solutions to the equation ψ(z)=q, where ψ is the Laplace exponent. Under additional regularity assumptions on the Lévy measure we obtain an asymptotic expression for these solutions. When the process is spectrally negative with bounded jumps, we derive a series representation for the scale function. In order to illustrate possible applications, we discuss the implementation of numerical algorithms and present the results of several numerical experiments.
Volume (Year): 122 (2012)
Issue (Month): 7 ()
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- Fourati, Sonia, 2012. "Explicit solutions of the exit problem for a class of Lévy processes; applications to the pricing of double-barrier options," Stochastic Processes and their Applications, Elsevier, vol. 122(3), pages 1034-1067.
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