Approximation of optimal ergodic dividend strategies using controlled Markov chains

Zhuo Jin*, Hailiang Yang, George Yin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

This study develops a numerical method to find optimal ergodic (long-run average) dividend strategies in a regimeswitching model. The surplus process is modelled by a regime-switching process subject to liability constraints. The regimeswitching process is modelled by a finite-time continuous-time Markov chain. Using the dynamic programming principle, the optimal long-term average dividend payment is a solution to the coupled system of Hamilton-Jacobi-Bellman equations. Under suitable conditions, the optimal value of the long-term average dividend payment can be determined by using an invariant measure. However, due to the regime switching, getting the invariant measure is very difficult. The objective is to design a numerical algorithm to approximate the optimal ergodic dividend payment strategy. By using the Markov chain approximation techniques, the authors construct a discrete-time controlled Markov chain for the approximation, and prove the convergence of the approximating sequences. A numerical example is presented to demonstrate the applicability of the algorithm.

Original languageEnglish
Pages (from-to)2194-2204
Number of pages11
JournalIET Control Theory and Applications
Volume12
Issue number16
DOIs
Publication statusPublished - 6 Nov 2018
Externally publishedYes

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