Phase-type Fitting of scale functions for spectrally negative Lévy processes. (English) Zbl 1291.60094

Summary: We study the scale function of the spectrally negative phase-type Lévy process. Its scale function admits an analytical expression and so do a number of its fluctuation identities. Motivated by the fact that the class of phase-type distributions is dense in the class of all positive-valued distributions, we propose a new approach to approximating the scale function and the associated fluctuation identities for a general spectrally negative Lévy process. Numerical examples are provided to illustrate the effectiveness of the approximation method.


60G51 Processes with independent increments; Lévy processes
60J75 Jump processes (MSC2010)
65C50 Other computational problems in probability (MSC2010)
Full Text: DOI arXiv


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