带状态切换的污染控制问题中混合极限环的最优性与可持续性
Optimality and sustainability of hybrid limit cycles in the pollution control problem with regime shifts
AI总结：
本文研究带周期性状态切换的污染控制问题，证明最优减排政策对应唯一混合极限环，并提出环境可持续解概念，说明其能在无限时间区间内同时实现最大收益与环境保护，而短视解长期失效。
摘要：
在本文中，我们考虑一个经历周期性状态切换的系统中的污染控制问题。我们首先证明，最优污染减排政策也是周期性的，并且由唯一的混合极限环描述。接着，我们引入环境可持续解的概念，并证明这种政策是唯一能够在稳定实现利润与确保环境保护之间取得最佳权衡的政策。与之相反，不具备环境可持续性的政策最终会陷入停滞。为了进一步说明我们的发现，我们将最优周期解与短视解进行比较。有趣的是，短视解在短期内能获得更高的总收益，但在长期内完全失效，而环境可持续政策在无限时间区间内既能获得最大收益，又能保护环境。
英文摘要：
In this paper, we consider the problem of pollution control in a system that undergoes regular regime shifts. We first show that the optimal policy of pollution abatement is periodic as well, and is described by the unique hybrid limit cycle. We next introduce the notion of an environmentally sustainable solution, and demonstrate that such a policy is the only one that yields the best possible trade-off between steadily achieving profit and ensuring environmental preservation. In contrast to that, the policy that is not environmentally sustainable eventually enters stagnation. To further illustrate our findings, we compare the optimal periodic solution with a myopic one. Interestingly enough, the myopic solution yields higher overall payoff in the short-run, but completely fails in the long-run, while the environmentally sustainable policy yields maximal payoff and preserves the environment over the infinite time interval.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
