Continuous-Time Methods for Integrated Assessment Models
Continuous-Time Methods for Integrated Assessment Models
复制标题
综合评估模型的连续时间方法
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
T. Lontzek
中科院分区：
文献类型：
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作者：
Y. Cai;K. Judd;T. Lontzek
连续时间是综合评估模型（IAM）旨在研究的经济和气候系统的上级代表。此外，连续时间表示很容易表达。连续时间模型通常通过时间离散化来求解，但离散化的细节会显著影响解的质量。数值分析文献提供了许多可靠的方法，应该使用，因为来自“直觉”的替代方案可能显着逊色。我们以著名的DICE模型为例。DICE使用10年时间步长。我们首先确定DICE的基本连续时间模型。其次，我们提出了数学和计算方法，将连续时间确定性完美预见模型转化为有限差分方程系统。虽然某些变换创建的有限差分系统看起来像离散时间动力系统，但唯一正确的方法是将有限差分系统视为连续时间问题的近似。DICE是一个例子，其中使用有限差分方法从数值分析产生远远优于上级近似比简单的离散时间系统。
Continuous time is a superior representation of both the economic and climate systems that Integrated Assessment Models (IAM) aim to study. Moreover, continuous-time representations are simple to express. Continuous-time models are usually solved by discretizing time, but the quality of a solution is significantly affected by the details of the discretization. The numerical analysis literature offers many reliable methods, and should be used because alternatives derived from "intuition" may be significantly inferior. We take the well-known DICE model as an example. DICE uses 10-year time steps. We first identify the underlying continuous-time model of DICE. Second, we present mathematical and computational methods for transforming continuous-time deterministic perfect foresight models into systems of finite difference equations. While some transformations create finite difference systems that look like a discrete-time dynamical system, the only proper way to view the finite difference system is as an approximation of the continuous-time problem. DICE is an example where the usage of finite difference methods from numerical analysis produces far superior approximations than do simple discrete-time systems.