Applications of Fractional Calculus in Economics

Dear Colleagues,

Standard equilibrium models are proving to be increasingly limited when it comes to capturing dynamics and the growing complexity of economic and financial systems. The very notions of equilibrium and pure rationality are incessantly challenged by reality: systemic events such as the 2007–2009 global financial crisis cannot be explained within the narrow borders of traditional models. It is precisely the economic and financial instability that has rekindled, among both researchers and practitioners, a widespread perception that alternative models are needed, more attentive to emphasize the adaptive behavior of economic agents acting with limited rationality and/or information.

In rethinking the very foundations of economic and financial modeling, a prominent role is played by fractal and multifractal models; compared to the classical approach, they show both better capacity and greater conceptual parsimony in representing the complex dynamics triggered by the interaction of economic agents. Notions such as data granularity, scale invariance, Hurst exponent, long-term memory, rough volatility and fractional Black–Scholes models now represent well-known tools that allow a deeper understanding of the mechanisms underlying many economic and financial processes. This advance is largely due to the increasing number of contributions devoted to investigating how fractals can improve the understanding of complex structures such as markets. Although the research in this field has achieved significant results on theoretical issues, as well as on many empirical aspects related to estimation and forecasting, much work still has to be done in order to build a sufficiently robust and convincing theoretical framework, where rational and behavioral economics can find a synthesis. Fractal models can potentially represent such a framework. The focus of this Special Issue is to continue to advance research on topics related to the theory of fractional models in economics and finance, to their implementation, estimation and forecasting. Topics that are invited for submission include (but are not limited to):

• Fractional/Multifractional stochastic processes in economics and finance
• Self-similarity and (multi)scaling
• (Generalized) Hurst exponent, Hölder regularity
• Rough volatility
• Fractional-order chaotic systems
• Fractional option prices

Prof. Dr. Sergio Bianchi
Guest Editor

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