We study a renewal theory approach to perpetual two-state switching problems with infinite value functions. Since the corresponding value functions are infinite, the problems fall outside the standard class of problems which can be analyzed using dynamic programming. Instead, we propose an alternative formulation of optimal switching theory in which optimality of a strategy is defined in terms of its long-term mean return, which can be determined using renewal theory. The approach is illustrated by examples in connection with trend-following strategies in finance.

中文翻译：

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具有无限值的两态切换问题的更新理论方法

我们研究了一种更新理论方法来解决具有无限值函数的永久二态切换问题。由于相应的价值函数是无限的，这些问题不属于可以使用动态规划分析的标准问题类别。相反，我们提出了最优转换理论的另一种表述，其中策略的最优性是根据其长期平均回报来定义的，这可以使用更新理论来确定。该方法通过与金融趋势跟踪策略相关的示例进行说明。