This paper is devoted to consumption-portfolio control problems with regime-switching-modulated habit formation. The formation of a habit depends on the current regime, which leads to time inconsistency in optimal control. General utility functions are used to evaluate the preference for the consumption net of the habit. To derive an analytical solution, we consider an enlarged financial market with Markov jump assets. Then, the time-inconsistent problem for pre-commitment controls is reduced to solving a regime-switching Hamilton–Jacobi–Bellman (HJB) equation. In seeking a time-consistent control, we investigate an alternate problem by means of multi-person sequential games with an essentially cooperative approach. The analytical expression of the time-consistent control is derived via a straightforward application of the pre-commitment control results. Moreover, the limit case in which the mesh size of time approaches zero is studied.

本文致力于通过制度转换调节习惯形成来解决消费组合控制问题。习惯的形成取决于当前的制度，这导致最佳控制的时间不一致。一般效用函数用于评估对习惯消费网的偏好。为了得出解析解，我们考虑了一个扩大的金融市场和马尔可夫跳跃资产。然后，预承诺控制的时间不一致问题被简化为求解状态切换的 Hamilton-Jacobi-Bellman (HJB) 方程。在寻求时间一致的控制时，我们通过采用本质上合作的方法的多人顺序游戏来研究另一个问题。时间一致控制的解析表达式是通过直接应用预承诺控制结果得出的。此外，研究了时间网格大小趋近于零的极限情况。