Numerical methods for dividend optimization usingregime-switching jump-diffusion models

Zhuo Jin; George Yin; Hailiang Yang

doi:10.3934/mcrf.2011.1.21

Article Contents

2011, Volume 1, Issue 1: 21-40. Doi: 10.3934/mcrf.2011.1.21

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Numerical methods for dividend optimization using regime-switching jump-diffusion models

1.
Department of Mathematics, Wayne State University, Detroit, Michigan 48202
2.
Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong

Received: July 31, 2010

Revised: September 30, 2010

Published: February 2011

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Abstract

This work develops numerical methods for finding optimal dividend policies to maximize the expected present value of dividend payout, where the surplus follows a regime-switching jump diffusion model and the switching is represented by a continuous-time Markov chain. To approximate the optimal dividend policies or optimal controls, we use Markov chain approximation techniques to construct a discrete-time controlled Markov chain with two components. Under simple conditions, we prove the convergence of the approximation sequence to the surplus process and the convergence of the approximation to the value function. Several examples are provided to demonstrate the performance of the algorithms.

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Mathematics Subject Classification: 93E20, 91B30, 91B70, 60H35, 65C05, 65C30.

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