掌握连续时间下的随机OLG模型
Mastering Stochastic OLG Models in Continuous Time
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中文总结 AI 辅助
本研究提出有限差分神经算子框架，结合神经网络与有限差分法优势，成功求解含个体及总体风险的连续时间OLG模型，为异质主体模型计算提供新手段。
中文摘要 AI 辅助
我们提出了一个综合框架，用于求解同时包含个体风险和总体风险的连续时间重叠世代（OLG）模型。我们通过主方程对均衡进行的一般刻画，作用于连续个体状态、年龄与财富的联合分布。我们的计算策略是将该分布的有限维表示作为神经网络的输入，神经网络继而输出（条件）价值函数的有限差分表示。这一思路可普遍应用于包含总体风险的异质主体模型，我们将其命名为有限差分神经算子。我们的方法结合了现代神经网络与传统有限差分方法的优势：在高维分布上无网格，且能控制低维状态变量的边界条件，此外还可施加形状约束。我们通过两个案例展示其灵活性：一是仅含总体风险的连续时间OLG模型，我们通过支撑函数刻画其分布；二是同时包含两类风险的OLG模型。
英文摘要
We propose a comprehensive framework for solving overlapping-generations (OLG) models in continuous time with both idiosyncratic and aggregate risk. Our general characterization of equilibrium through the master equation operates on the joint distribution over the continuous idiosyncratic states, age and wealth. Our computational strategy is to take a finite-dimensional representation of this distribution as an input of a neural net which in turn outputs a finite-difference representation of the (conditional) value function. This idea can be applied generally to heterogeneous agent models with aggregate risk, and we call it finite-difference neural operator. Our method combines advantages from modern neural nets and traditional finite-difference methods: It is grid-free in the high-dimensional distribution, and retains control on boundary conditions in low-dimensional state variables. Moreover, our method is able to enforce shape constraints. We showcase its flexibility by solving a continuous-time OLG model with aggregate risk alone where we characterize the distribution by its supporting function; and to an OLG model with both types of risk.
