SIAM Journal on Control and Optimization, Volume 59, Issue 1, Page 185-222, January 2021.
This paper investigates the impulse cash-flow withdrawal (dividend distribution or consumption) optimization problem for a broad class of growth restricted linear diffusions with drift and volatility dependent on both the level of surplus and the environment/economy regime (described by a Markov chain). There are proportional and fixed costs associated with each cash-flow withdrawal transaction, and the objective of the optimization problem is to determine the optimal policy that maximizes the expected total cumulative discounted cash-flow withdrawals (dividend payments/consumption) minus expenses. This work extends all the existing work on the same problem under the diffusion setting by extending the underlying dynamics to a much more general class of Markov modulated diffusions and unifies the existing work on optimal impulse dividend control. We show that when there are two regimes, the value function, as a function of the initial cash reservoir and the initial environmental state, can be determined by solving a set of second order ordinary differential equations. We further show that either the optimal strategy is a regime switching lump-sum dividend barrier strategy or there exists no optimal strategies.

中文翻译：

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具有区域切换的生长受限线性扩散的最优脉冲控制

SIAM控制与优化杂志，第59卷，第1期，第185-222页，2021年1月。
本文研究了一类广泛的增长受限线性扩散的冲动现金流量提取（股息分配或消费）优化问题，其中线性波动的波动性和波动性取决于盈余水平和环境/经济体制（由马尔可夫链描述） 。每个现金流量取款交易都有成比例的固定成本，最优化问题的目的是确定使预期的总累计现金流量折现（股息支付/消费）减去支出的预期最大化的最优策略。这项工作通过将基本动力学扩展到一个更通用的马尔可夫调制扩散类别，并扩展了现有的关于最优脉冲红利控制的工作，从而扩展了扩散设置下关于同一问题的所有现有工作。我们表明，当存在两种状态时，可以通过求解一组二阶常微分方程来确定作为初始现金储备和初始环境状态的函数的价值函数。我们进一步表明，要么最优策略是一种政权转换总和红利屏障策略，要么不存在最优策略。