The Hamilton-Jacobi-Bellman Equation in Economic Dynamics with a Non-Smooth Fiscal Policy
We consider a class of economic growth models that includes the classical Ramsey--Cass--Koopmans capital accumulation model and verify that, under several assumptions, the value function of the model is the unique viscosity solution to the Hamilton--Jacobi--Bellman equation. Moreover, we discuss a solution method for these models using differential inclusion, where the subdifferential of the value function plays an important role. Next, we present an assumption under which the value function is a classical solution to the Hamilton--Jacobi--Bellman equation, and show that many economic models satisfy this assumption. In particular, our result still holds in an economic growth model in which the government takes a non-smooth Keynesian policy rule.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
On the Fragility of the Basis on the Hamilton-Jacobi-Bellman Equation in Economic Dynamics
In this paper, we provide an example of the optimal growth model in which there exist infinitely many solutions to the Hamilton-Jacobi-Bellman equation but the value function does not satisfy this equation. We consider t…
On the Basis of the Hamilton-Jacobi-Bellman Equation in Economic Dynamics
We consider the classical Ramsey-Cass-Koopmans capital accumulation model and present three examples in which the Hamilton-Jacobi-Bellman (HJB) equation is neither necessary nor sufficient for a function to be the value …
Computation of Reachable Sets Based on Hamilton-Jacobi-Bellman Equation with Running Cost Function
A novel method for computing reachable sets is proposed in this paper. In the proposed method, a Hamilton-Jacobi-Bellman equation with running cost functionis numerically solved and the reachable sets of different time h…
Deep neural network approximation for high-dimensional parabolic Hamilton-Jacobi-Bellman equations
The approximation of solutions to second order Hamilton--Jacobi--Bellman (HJB) equations by deep neural networks is investigated. It is shown that for HJB equations that arise in the context of the optimal control of cer…
Deep Graphic FBSDEs for Opinion Dynamics Stochastic Control
In this paper, we present a scalable deep learning approach to solve opinion dynamics stochastic optimal control problems with mean field term coupling in the dynamics and cost function. Our approach relies on the probab…
LEMMA