Problem
Research questions and friction points this paper is trying to address.
stochastic OLG models
continuous time
idiosyncratic risk
aggregate risk
heterogeneous agents
Mastering Stochastic OLG Models in Continuous Time
🤖 AI Summary
This study addresses the challenge of computing equilibria in continuous-time overlapping generations (OLG) models featuring both idiosyncratic and aggregate risks. To this end, it introduces a novel “finite-difference neural operator” method that formulates equilibrium via a master equation, representing the joint distribution over continuous age, wealth, and individual states through a support function fed into a neural network, which then outputs a finite-difference representation of the conditional value function. By integrating the high-dimensional approximation capacity of neural networks with the finite-difference method’s precise handling of boundary conditions and economic shape constraints, the approach establishes a mesh-free framework for solving high-dimensional distributional equilibria. The method is applied to two OLG settings—one with only aggregate risk and another incorporating both idiosyncratic and aggregate risks—demonstrating its flexibility, accuracy, and scalability.
📝 Abstract
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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
finite-difference neural operator
continuous-time OLG models
heterogeneous agent models
master equation
shape constraints
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