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

2010/05/01 by Masahiko Egami, Egami, Masahiko, Kazutoshi Yamazaki +1 · 3 citations
Decision Sciences · Economics, Econometrics and Finance · #Probability and Risk Models #Stochastic processes and financial applications #Financial Risk and Volatility Modeling

paper · pdf · doi:10.48550/arxiv.1005.0064

Abstract

We study the scale function of the spectrally negative phase-type Levy 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 Levy process. Numerical examples are provided to illustrate the effectiveness of the approximation method.

Citations

• On the Convergence Properties of the EM Algorithm
• Wiener-Hopf Factorization for a Family of Lévy Processes Related to Theta Functions
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