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We study the Wiener-Hopf factorization for Levy processes with boundedpositive jumps and arbitrary negative jumps. Using the results from the theoryof entire functions of Cartwright class we prove that the positive Wiener-Hopffactor can be expressed as an infinite product in terms of the solutions to theequation $\psi(z)=q$, where $\psi$ is the Laplace exponent of the process.Under some additional regularity assumptions on the Levy measure we obtain anasymptotic expression for these solutions, which is important for numericalcomputations. In the case when the process is spectrally negative with boundedjumps, we derive a series representation for the scale function in terms of thesolutions to the equation $\psi(z)=q$. To illustrate possible applications wediscuss the implementation of numerical algorithms and present the results ofseveral numerical experiments.

On the Wiener-Hopf factorization for Levy processes with bounded positive jumps