Forum Numerica - Pr. Davide La Torre: Self-Similar Fractal Measures in Multi-Sector Endogenous Growth Models

More than thirty years later the seminal work of Boldrin and Montrucchio (1986), it is now well known that also traditional (macro)economic models may give rise to complicated dynamics, including random dynamics eventually converging to (possibly singular) invariant measures supported on fractal sets.
In this talk we analyze two types of stochastic discrete time multi-sector endogenous growth models, namely a basic Lucas-Uzawa (1988) model and an extended three-sector version as in La Torre and Marsiglio (2010). We focus on the dynamics of the capital ratio variables, and we show that, through appropriate log-transformations, they can be converted into affine iterated function systems converging to an invariant distribution supported on some fractal compact set. This proves that also the steady state of endogenous growth models — i.e., the stochastic balanced growth path equilibrium — might have a fractal nature.
We also provide some sufficient conditions under which the associated self-similar measures turn out to be either singular or absolutely continuous.

Reference: H.Kunze, D.La Torre, F.Mendivil, E.R.Vrscay, Fractal-based Methods in Analysis, Springer, 2012.

Davide La Torre, PhD, HDR, is a Mathematician, Researcher, and University Professor.
Currently he holds the position of Full Professor and Director of the Artificial Intelligence for Business Institute at SKEMA Business School, Sophia Antipolis Campus, France.
His research and teaching interests include Applied Mathematics, Artificial Intelligence, Business Analytics, Machine Learning, Mathematical and Statistical Modelling, and Operations Research.
He holds an HDR (Habilitation à Diriger des Recherches) in Applied Mathematics from Université Côte d'Azur, Nice, France (2021), a Doctorate in Computational Mathematics and Operations Research from the University of Milan, Milan, Italy (2001) as well as professional certificates in Analytics from the Massachusetts Institute of Technology, Cambridge, USA.
In the past he held permanent, adjunct, and visiting university professor positions in Europe, Canada, Middle East, Central Asia, and Australia. He also served as Departmental Chair and Program Head at several universities including the University of Milan (Italy), Khalifa University (UAE), University of Dubai (UAE), and Nazarbayev University (Kazakhstan).
He has 180 publications in Scopus, most of them published in high IF journals ranging from Engineering to Business.
https://scholar.google.fr/citations?user=rTwiT3gAAAAJ&hl=fr