<p style='text-indent:20px;'>The economy-climate interaction and an appropriate mitigation policy for climate protection have been treated in various types of scientific modeling. Here, we specifically focus on the seminal work by Nordhaus [<xref ref-type="bibr" rid="b14">14</xref>, <xref ref-type="bibr" rid="b15">15</xref>] on the economy-climate link. We extend the Nordhaus type model to include optimal policies for mitigation, adaptation and infrastructure investment studying the dynamics of the transition to a low fossil-fuel economy. Formally, the model gives rise to an optimal control problem consisting of a dynamic system with five-dimensional state vector representing stocks of private capital, green capital, public capital, stock of brown energy in the ground, and carbon emissions. The objective function captures preferences over consumption but is also impacted by atmospheric <inline-formula><tex-math id="M1">\begin{document}$ \mathrm{CO}_2 $\end{document}</tex-math></inline-formula> and by mitigation and adaptation policies. Given the numerous challenges to climate change policies the control vector is eight-dimensional comprising mitigation, adaptation and infrastructure investment. Our solutions are characterized by turnpike property and the optimal policies that accomplish the objective of keeping the <inline-formula><tex-math id="M2">\begin{document}$ \mathrm{CO}_2 $\end{document}</tex-math></inline-formula> levels within bound are characterized by a significant proportion of investment in public capital going to mitigation in the initial periods. When initial levels of <inline-formula><tex-math id="M3">\begin{document}$ \mathrm{CO}_{2} $\end{document}</tex-math></inline-formula> are high, adaptation efforts also start immediately, but during the initial period, they account for a smaller proportion of government's public investment.</p>

中文翻译：

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具有适应和缓解的全球气候变化模型的最佳控制

<p style='text-indent:20px;'>经济与气候的相互作用以及气候保护的适当减缓政策已在各种类型的科学建模中得到处理。在这里，我们特别关注 Nordhaus [<xref ref-type="bibr" rid="b14">14</xref>, <xref ref-type="bibr" rid="b15">15< /xref>] 在经济气候链接上。我们扩展了 Nordhaus 模型，以包括缓解、适应和基础设施投资的最佳政策，研究向低化石燃料经济过渡的动态。形式上，该模型产生了一个最优控制问题，该问题由一个动态系统组成，该系统具有五维状态向量，代表私人资本存量、绿色资本、公共资本、地下棕色能源存量，和碳排放。目标函数捕捉消费偏好，但也受到大气 <inline-formula><tex-math id="M1">\begin{document}$ \mathrm{CO}_2 $\end{document}</tex- math></inline-formula> 以及缓解和适应政策。鉴于气候变化政策面临众多挑战，控制向量是八维的，包括缓解、适应和基础设施投资。我们的解决方案的特点是收费公路属性和实现保持 <inline-formula><tex-math id="M2">\begin{document}$ \mathrm{CO}_2 $\end{document }</tex-math></inline-formula> 限制范围内的水平的特点是，在初始阶段有很大比例的公共资本投资用于缓解。当 <inline-formula><tex-math id="M3">\begin{document}$ \mathrm{CO}_{2} $\end{document}</tex-math></inline- 的初始级别公式>高，适应工作也立即启动，但在初期，它们占政府公共投资的比例较小。</p>