A Dive Into the Asymptotic Analysis Theory: a Short Review from Fluids to Financial Markets

Abstract

The asymptotic analysis theory is a powerful mathematical tool employed in the study of complex systems. By exploring the behavior of mathematical models in the limit as certain parameters tend toward infinity or zero, the asymptotic analysis facilitates the extraction of simplified limit-equations, revealing fundamental principles governing the original complex dynamics. We will highlight the versatility of asymptotic methods in handling different scenarios, ranging from fluid mechanics to biological systems and economic mechanisms, with a greater focus on the financial markets models. This short overview aims to convey the broad applicability of the asymptotic analysis theory in advancing our comprehension of complex systems, making it an indispensable tool for researchers and practitioners across different disciplines. In particular, such a theory could be applied to reshape intricate financial models (e.g., stock market volatility models) into more manageable forms, which could be tackled with time-saving numerical implementations.