A Single-Sector Stochastic Model of Economics

Oleg Malafeyev and Sergei Nemnyugin
Department of Computational Physics, Sankt-Petersburg State University
nemnugin@snoopy.niif.spb.su

Abstract

In this paper we shall construct two classes of single-sector stochastic models of economics with perfect competition. The first one is created by inclusion of the stochastic evolution of exogenous variables into the well known deterministic model. The perfect competition requires maximization of the income at any moment. The resulting linear stochastic differential equation may be solved by standard methods. The second approach requires optimization of the stochastic income functional when it is supposed that exogenous variables follows stochastic differential equation. This problem may be solved by dynamic programming method but application of the computational techniques developed in the computational physics may be of interest too.