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

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.

33 pages, 8 figures

References in corpus (4)

• On the optimal dividend problem for a spectrally negative Lévy process
• On optimality of the barrier strategy in de Finetti's dividend problem for spectrally negative Lévy processes
• Wiener-Hopf factorization and distribution of extrema for a family of Lévy processes
• Meromorphic Levy processes and their fluctuation identities