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

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 absolut...

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Bibliographic Details
Published in:Mathematical problems in engineering 2020, Vol.2020 (2020), p.1-21
Main Authors: Hu, Chunhua, Xie, Tianhao, Huang, Wen-Yi
Format: Article
Language:English
Subjects:
Domains
Euler-Lagrange equation
Risk
Wealth distribution
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Summary: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.
ISSN:1024-123X
1563-5147
DOI:10.1155/2020/4353025