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

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  • Masahiko Egami
  • Kazutoshi Yamazaki

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.

Suggested Citation

  • Masahiko Egami & Kazutoshi Yamazaki, 2010. "Solving Optimal Dividend Problems via Phase-Type Fitting Approximation of Scale Functions," Discussion papers e-10-011, Graduate School of Economics Project Center, Kyoto University.
    • Handle: RePEc:kue:dpaper:e-10-011
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    References listed on IDEAS

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    Cited by:

    1. Tim Siu-Tang Leung & Kazutoshi Yamazaki, 2010. "American Step-Up and Step-Down Default Swaps under Levy Models," Papers 1012.3234, arXiv.org, revised Sep 2012.

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    More about this item

    Keywords

    De Finetti’s dividend problem; phase-type models; Meromorphic Lévy processes; Spectrally negative Lévy processes; Scale functions;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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