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On the Wiener-Hopf factorization for Lévy processes with bounded positive jumps. (English) Zbl 1246.60072

Summary: 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 \(\psi (z)=q\), where \(\psi \) 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.

MSC:

60G51 Processes with independent increments; Lévy processes
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