Phase-type fitting of scale functions for spectrally negative Lévy processes

• Autores: Masahiko Egami, Kazutoshi Yamazaki
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 264, Nº 1, 2014, págs. 1-22
• Idioma: inglés
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• Resumen

  • 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.