• Agent based models
• monetary policy
• Quantitative Easing

Physics has long served as an inspiration for economists in developing and in-
terpreting their theories, providing them with opportunities to draw analogies
and, later on, analytical tools to solve problems and formulate theories. From
this history of one-way influences, a new discipline emerged in the 1960s called
econophysics, which aimed to solidify this connection.
Econophysics primarily focuses on two major areas, which may have points
of overlap, especially in their methodologies. On one hand, there is the study
of financial markets, using tools from probability theory and analyzing large
datasets. On the other hand, it examines the society of economic actors as a
whole, where each actor is modeled and interacts with others. These models,
known as agent-based models, can be dedicated to investigating various issues,
such as macroeconomic phenomena or the study of income and wealth inequali-
ties within a society.
This thesis will focus on the study of the second part of econophysics, ad-
dressing two distinct economic problems that have captured the attention of
the academic debate. On one hand, standard macroeconomic theory has shown
its limitations on multiple fronts, especially in predicting, explaining, and pro-
viding solutions to the severe economic crisis of 2008. On the other hand, the
monumental work, primarily empirical, by Thomas Piketty in ”Capital in the
Twenty-First Century” has brought the issue of inequality to the forefront as a
research topic that economists had long neglected. This issue has become urgent
and of public relevance, particularly due to the significant growth in inequality
in wealthy countries over the past forty years or so.
After an introduction highlighting how physics has progressively entered the field
of economics, the Dragulescu-Yakovenko model will be presented. This model is
clearly inspired by statistical mechanics and is used to describe the distribution
of resources in a given society. Based on this model, further investigations
and numerical simulations will be conducted to study the thermalization of the
system. Subsequently, a broader mathematical framework of the model will be
provided to enable the ultimate goal of the thesis, which is the study of the effects
of Quantitative Easing on wealth distribution. This study is presented following
other numerical explorations of the Dragulescu-Yakovenko model. In particular,
in the last chapter, a comparison will be made between the Krugman model for Quantitative Easing and the attempt to account for the same phenomenon
through an Agent-Based model.