Open AccessApproximation of optimal ergodic dividend strategies using controlled Markov chains
Author(s) -
Jin Zhuo,
Yang Hailiang,
Yin George
Publication year - 2018
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2018.5394
Subject(s) - markov chain , ergodic theory , mathematical optimization , bellman equation , markov process , mathematics , invariant measure , markov decision process , dynamic programming , convergence (economics) , optimal control , measure (data warehouse) , dividend , control theory (sociology) , computer science , finance , economics , control (management) , mathematical analysis , statistics , database , artificial intelligence , economic growth
This study develops a numerical method to find optimal ergodic (long‐run average) dividend strategies in a regime‐switching model. The surplus process is modelled by a regime‐switching process subject to liability constraints. The regime‐switching 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.