Sergio Focardi - Böcker

Fractional Calculus and Fractional Processes with Applications to Financial Economics presents the theory and application of fractional calculus and fractional processes to financial data. Fractional calculus dates back to 1695 when Gottfried Wilhelm Leibniz first suggested the possibility of fractional derivatives. Research on fractional calculus started in full earnest in the second half of the twentieth century. The fractional paradigm applies not only to calculus, but also to stochastic processes, used in many applications in financial economics such as modelling volatility, interest rates, and modelling high-frequency data. The key features of fractional processes that make them interesting are long-range memory, path-dependence, non-Markovian properties, self-similarity, fractal paths, and anomalous diffusion behaviour. In this book, the authors discuss how fractional calculus and fractional processes are used in financial modelling and finance economic theory. It provides a practical guide that can be useful for students, researchers, and quantitative asset and risk managers interested in applying fractional calculus and fractional processes to asset pricing, financial time-series analysis, stochastic volatility modelling, and portfolio optimization.

Provides the necessary background for the book's content as applied to financial economics Analyzes the application of fractional calculus and fractional processes from deterministic and stochastic perspectives

A comprehensive look at causality’s theoretical and practical aspects in economics and finance.Causal Modeling for Finance and Business presents causality’s theoretical and practical aspects in economics and finance. Frank Fabozzi and Sergio Focardi offer a foundation for understanding causal relationships and their importance in complex systems. Topics include the theory of graphs, probabilistic frameworks, structural causal models, algorithms for learning causal structures, and the empirical testing of these models.The book emphasizes applying and deploying causal models in real-world business and investment scenarios. However, it offers also a novel theoretical perspective on causal modeling. Causation is not a law of nature, but it is a characteristic of causal systems. If we accept the modern idea of causation as manipulability, causal systems are characterized by causal relationships as well as purely descriptive functional relationships.The book addresses a critical gap in understanding and applying causal reasoning in complex systems. While correlations have often been relied upon in data analysis, decision-making in business and economics demands a deeper understanding of causation and functional relationships to drive actionable outcomes.The book’s objective is to provide a comprehensive resource that bridges foundational theories and practical applications of causal models. By integrating recent advancements in artificial intelligence, probabilistic logic, and graph theory, the authors offer a robust framework for researchers, practitioners, and decision-makers to harness the power of causality in solving intricate problems.