# Limit Theorems for Individual-Based Models in Economics and Finance

Daniel Remenik

Arxiv ID: 0810.2813•Last updated: 10/15/2020

There is a widespread recent interest in using ideas from statistical physics
to model certain types of problems in economics and finance. The main idea is
to derive the macroscopic behavior of the market from the random local
interactions between agents. Our purpose is to present a general framework that
encompasses a broad range of models, by proving a law of large numbers and a
central limit theorem for certain interacting particle systems with very
general state spaces. To do this we draw inspiration from some work done in
mathematical ecology and mathematical physics. The first result is proved for
the system seen as a measure-valued process, while to prove the second one we
will need to introduce a chain of embeddings of some abstract Banach and
Hilbert spaces of test functions and prove that the fluctuations converge to
the solution of a certain generalized Gaussian stochastic differential equation
taking values in the dual of one of these spaces.

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