Numerical Methods for the Yard-Sale Model of Wealth Distribution.
Wang, Hongyan.
2019
-
Wealth inequality is one of the most serious issues in the world today. Much of the research in this area is dedicated to understand the dynamics of wealth distribution. An important and successful class of wealth distribution models, that have been analyzed using mathematical methods of statistical physics, are called Asset Exchange Models (AEMs). In my thesis, I study a particular AEM called the ... read moreYard-Sale Model (YSM), and discuss several numerical methods for its solution. In Chapter 2, I will describe the basic YSM, demonstrate how to extend it with the addition of two important features, namely redistribution and Wealth-Attained Advantage (WAA), to obtain the Extended Yard-Sale Model (EYSM). I will derive the corresponding non-linear Fokker-Planck equation that describes the evolution of the agent density function for this model. In Chapter 3, we discuss how to implement Monte Carlo simulation to understand the dynamics of the EYSM wealth distribution in microlevel. In Chapter 4, we discuss how to use the shooting method to solve for the steady-state solutions of the Fokker-Planck equation for the EYSM. In Chapter 5, we show how to implement the Finite-Element algorithm to solve for the time-dependent solutions to the EYSM. With the Finite-Element algorithm, we are able to not only study the time-dependent behaviors of the EYSM, but also build the large database for the solutions to the EYSM. In Chapter 6, we extend the EYSM to the Affine Wealth Model (AWM) for simulating negative wealth, and show our results for fitting the AWM to the European wealth distribution data from the Household Finance and Consumption Survey (HFCS) conducted by the European Central Bank (ECB).
Thesis (Ph.D.)--Tufts University, 2019.
Submitted to the Dept. of Mathematics.
Advisor: Bruce Boghosian.
Committee: James Adler, Xiaozhe Hu, and Peter Coveney.
Keyword: Mathematics.read less - ID:
- mc87q3746
- To Cite:
- TARC Citation Guide EndNote
