A Distributionally Robust Economic Dynamics Model And Its Numerical Solution

Modern economic theory views the economy as a dynamical system in which rational decisions are made in the face of uncertainties. Optimizing decisions over time on market behavior such as consumption, investment, labor supply, and technology innovation is of practical importance. The neoclassical growth model is a classical model in economic dynamics and macro-economy. The related theory analyzes the effect of capital accumulation^population growth and technical innovation on economy growth. There have been a lot of methods for undertaking the neoclassical growth model with uncertainties since the1990’s, including the method of combining spline approximation and iteration.Stochastic programming refers to the decision-making model, where the distribution function is known while some parameters are uncertain. When the distribution function is unknown and the decision should be optimal in the worst case, the corresponding programming becomes robust optimization and the distributionally robust optimization, respectively. Robust optimization refers to finding the optimal value of the objective function under the worst situation of all possible uncertainties, when all the constraints are satisfied. When only parts of the information on the probability distribution of the uncertain variable are known, such as the first-order moment, second-order moment and support set, and the aim is to find the worst-case solution under all possible distributions, the corresponding programming is distributionally robust optimization.This paper applies the idea of distributionally robust optimization on the neoclassical growth model with leisure choice. Using Bellman’s principle of optimality, we build the distributionally robust dynamic programming model. We derived the Euler equation by the first-order optimality condition. By applying the duality of the semi-infinite programming, we translate the optimization problem on the right side of the Euler equation into semi-infinite programming and solve it. In this paper, we use the composite1-dimensional cubic splines to approximate the policy function, solve the Euler equation by Newton method, and finally get the numerical solution of the policy function.