Approximation of optimal ergodic dividend strategies using controlled Markov chains
Approximation of optimal ergodic dividend strategies using controlled Markov chains
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DOI：
10.1049/iet-cta.2018.5394
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发表时间：
2018-08
影响因子：
2.6
通讯作者：
Z. Jin;Hailiang Yang;G. Yin
中科院分区：
文献类型：
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作者：
Z. Jin;Hailiang Yang;G. Yin
本研究发展了一种数值方法来寻找制度转换模型中最优的遍历（长期平均）股利策略。盈余过程是一个受负债约束的制度转换过程的模型。状态切换过程用有限时间连续马尔可夫链来建模。利用动态规划原理，最优长期平均股利支付是Hamilton-Jacobi-Bellman方程耦合系统的解。在适当的条件下，可以用不变测度确定长期平均股利支付的最优值。然而，由于状态的切换，获得不变测度是非常困难的。目标是设计一个数值算法来近似最优遍历股利支付策略。利用马尔可夫链逼近技术，构造了一个离散时间控制的马尔可夫链，并证明了逼近序列的收敛性。通过数值算例验证了该算法的适用性。
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.