Essays on Metric Spaces and Macro-Finance [védés előtt]

Abstract

The dissertation framework consists of four chapters and it is written in essay format, where the aim is to perform a theoretical and quantitative analysis using mathematical concepts and macro-finance approaches. The dissertation presents evidence of two published papers in D1 (2024) and Q2 (2025) journals related to the topic of Chapter 2. and 4. We can see in every chapter a minimum problem, where the purpose is to reach an optimal minimum level. Chapter 1. introduces the main mathematical concepts in order to understand the second chapter of Mosco convergence in Cartan Alexandrov Topogonov or CAT(1)-space, where the reader could imagine a geometric shape (very similar to a geometric ball) with it’s important trigonometric angles, semi-convex functions, sequence of these functions and the associated gradient flows. Chapter 2. relies on the mathematical concepts and characteristics from Chapter 1. and incorporates these mentioned features into the Mosco convergence of CAT(1)-space. Particularly, the Mosco convergence of a sequence of semi-convex lower semi-continuous functions