For solving the regime switching utility maximization, Fu et al. (Eur J Oper Res 233:184–192, 2014) derive a framework that reduce the coupled Hamilton–Jacobi–Bellman (HJB) equations into a sequence of decoupled HJB equations through introducing a functional operator. The aim of this paper is to develop the iterative finite difference methods (FDMs) with iteration policy to the sequence of decoupled HJB equations derived by Fu et al. (2014). The convergence of the approach is proved and in the proof a number of difficulties are overcome, which are caused by the errors from the iterative FDMs and the policy iterations. Numerical comparisons are made to show that it takes less time to solve the sequence of decoupled HJB equations than the coupled ones.

为了解决方案切换效用最大化，Fu等。（Eur J Oper Res 233：184–192，2014）推导了一个框架，该框架通过引入函数算子，将耦合的Hamilton–Jacobi–Bellman（HJB）方程简化为一系列解耦的HJB方程。本文的目的是开发具有迭代策略的迭代有限差分法（FDM），以解决Fu等人解耦的HJB方程的序列。（2014）。证明了该方法的收敛性，并且在证明中克服了许多困难，这些困难是由迭代FDM和策略迭代产生的错误引起的。数值比较表明，解耦的HJB方程序列所需的时间少于耦合方程组。