Solving Optimal Dividend Problems via Phase-Type Fitting Approximation of Scale Functions

Masahiko Egami and Kazutoshi Yamazaki

Discussion papers from Graduate School of Economics Project Center, Kyoto University

Abstract: The optimal dividend problem by De Finetti (1957) has been recently generalized to the spectrally negative Lévy model where the implementation of optimal strategies draws upon the computation of scale functions and their derivatives. This paper proposes a phase-type fitting approximation of the optimal strategy. We consider spectrally negative Lévy processes with phase-type jumps as well as meromorphic Lévy processes (Kuznetsov et al., 2010a), and use their scale functions to approximate the scale function for a general spectrally negative Lévy process. We obtain analytically the convergence results and illustrate numerically the effectiveness of the approximation methods using examples with the spectrally negative Lévy process with i.i.d. Weibull-distributed jumps, the β-family and CGMY process.

Keywords: De Finetti’s dividend problem; phase-type models; Meromorphic Lévy processes; Spectrally negative Lévy processes; Scale functions (search for similar items in EconPapers)
JEL-codes: C61 D81 G22 (search for similar items in EconPapers)
Pages: 34 pages
Date: 2010-12
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:kue:dpaper:e-10-011

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