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Mathematical Control and Related Fields (MCRF)
 

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

Pages: 21 - 40, Volume 1, Issue 1, March 2011      doi:10.3934/mcrf.2011.1.21

 
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Zhuo Jin - Department of Mathematics, Wayne State University, Detroit, Michigan 48202, United States (email)
George Yin - Department of Mathematics, Wayne State University, Detroit, Michigan 48202, United States (email)
Hailiang Yang - Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong, China (email)

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.

Keywords:  Jump diffusion, dividend policy, regime switching, stochastic control.
Mathematics Subject Classification:  93E20, 91B30, 91B70, 60H35, 65C05, 65C30.

Received: August 2010;      Revised: October 2010;      Available Online: March 2011.

 References