Toru Maruyama Livres

Focusing on the intersection of Fourier analysis and dynamic economic theories, this monograph delves into business cycles through the Kaldor theory and Slutsky effect. It explores Kaldor's nonlinear differential equations and the Hopf-bifurcation theorem to explain economic fluctuations, while Slutsky's approach examines periodic movements from random shocks. The book aims to rigorously justify these theories, presenting essential Fourier analysis concepts systematically. It is accessible to readers with a background in analysis, even if they lack economic expertise.

The book explores advanced mathematical concepts and their applications in economics, focusing on mass transportation problems, functional evolution equations, and nonlinear matrix theory. It delves into optimization techniques involving non-C1 constraints and discusses the Monte Carlo method for pricing financial derivatives. Additionally, it provides a historical perspective on the development of mathematical economics in Vienna during the interwar period, highlighting significant contributions and theoretical advancements in the field.

This series aims to connect mathematicians seeking challenges from economic theories with economists in need of mathematical tools for their research, highlighting the mutual influence between economics and mathematics in addressing constrained optimization and equilibrium problems.