The Investigation of a Wealth Distribution Model on Isolated Discrete Time Domains

Abstract

A wealth distribution model on isolated discrete time domains, which allows the wealth to exchange at irregular time intervals, is used to describe the effect of agent’s trading behavior on wealth distribution. We assume that the agents have different degrees of risk aversion. The hyperbolic absolute risk aversion (HARA) utility function is employed to describe the degrees of risk aversion of agents, including decreasing relative risk aversion (DRRA), increasing relative risk aversion (IRRA), and constant relative risk aversion (CRRA). The effect of agent’s expectation on wealth distribution is taken into account in our wealth distribution model, in which the agents are allowed to adopt certain trading strategies to maximize their utility and improve their wealth status. The Euler equation and transversality condition for the model on isolated discrete time domains are given to prove the existence of the optimal solution of the model. The optimal solution of the wealth distribution model is obtained by using the method of solving the rational expectation model on isolated discrete time domains. A numerical example is given to highlight the advantages of the wealth distribution model.

The Study of a Wealth Distribution Model with a Linear Collision Kernel

“…Scholars apply different empirical studies to illustrate that the wealth distribution in the highincome range follows Pareto distribution, while in bulk ranges, it follows a Gibbs distribution, a Gamma distribution, or a log-normal distribution [2]. ese results inspire them to find a theory to explain the universality of wealth distribution [3][4][5]. In particular, employing the kinetic theory of rarefied gases to consider wealth distribution in closed systems can better explain the fat tail of wealth distribution in the economy [5][6][7][8][9].…”