Numerical Solutions to a Stochastic Growth Model Based on the Evolution of a Radial Basis Network

Abstract

This chapter introduces a new heuristics for solving the optimal consumption path in one-sector growth model, a typical stochastic dynamical optimization problem in economics. The proposed method avoids the ex-ante specification of a functional form for the policy function that solves the optimization problem. This novel approach has an advantage over other approaches like the Linear Quadratic Approximation (LQA) and the Parameterized Expectation (PE) methods. Instead, the functional form arises endogenously according to the characteristic of the problem the method is seeking to deal with. The heuristics combines Radial Basis Network (RBN) as a. representation of the potential solutions and an Evolutionary Strategy (ES) as a mechanism to prune the search space. Experiments were performed on different versions of a stochastic growth model and some satisfactory results were consequently obtained. In most cases the approximation obtained with the proposed method indeed outperforms the approximation reached by both the LQA and PE methods, based on not only one criterion but several different quality criteria.