Italian Abstract: Questo lavoro si propone il compito di individuare un approccio alternativo (in termini di algoritmo matematico) in grado di determinare con velocità (i.e. di convergere nel giro di poche iterazioni) il valore della volatilità implicita delle opzioni. Tale valore è di...

Questo lavoro si propone il compito di illustrare l'argomento di in maniera sufficientemente semplice e completa ed è corredato da esercizi per l'acquisizione delle tecniche computazionali relative. L'ottimizzazione è applicabile a problemi decisionali modellabili in termini di funzioni di...

Complex systems are characterized by deterministic laws (which often may be hidden) and randomness. A tool to analyse those systems is recurrence quantification analysis (RQA). RQA does not rely on any sort of assumption of stationarity and is not sensitive to singularities and transitions. It...

In this chapter, we outline the reasons why economics has been concerned with non-linear dynamics, with a particular focus on business cycles and on economic growth. Using varying perspectives, we discuss the salient historical mathematical approaches to the problem and the results that were...

As mentioned in the Introduction, Sect. 1.2, the objective of this book is twofold: to provide a personal specification of a business cycle model within the Kaldor-Kalecki framework (see Chap. 16) and to choose a chaotic specification of the Harrod model (Sportelli and Celi (Metroeconomica...

In this chapter, we describe growth and cycles in economics as a struggle between capitalists and workers. We first present the Phillips curve (which statistically relates unemployment with the rate of change of nominal wages) and then the Goodwin model. The latter reinterprets, in economical...

This chapter is dedicated to describe RQA applications in detecting spatio-temporal recurrent patterns of dynamical regimes of economic time series. Here we investigate the nature of economic dynamics and specifically of business cycles Orlando and Zimatore (Chaos, Solitons Fractals 110:82–94,...

After having illustrated in Chap. 13 the Harrod’s model and a chaotic specification of it, in this Chapter we are going to prove that (1) real data could be obtained by a suitable calibration of model’s parameters, (2) the calibrated model confirms theoretical predictions (Orlando and Della...