This book includes contributions about mathematics, physics, philosophy of science, economics and finance and resulted from the Summer School Complexity and Emergence: Ideas, Methods, with a Special Attention to Economics and Finance held in Lake Como School of Advanced Studies, on 2227 July 2018.

The aim of the book is to provide useful instruments from the theory of complex systems, both on the theoretical level and the methodological ones, profiting from knowledge and insights from leading experts of different communities. It moves from the volume editors' conviction that to achieve progress in understanding socio-economical as well as ecological problems of our complex word such preparation is needed, together with a critical reconsideration of our basic scientific and economical approach.

The potential readers are primarily master and doctorate students of mathematics, information sciences, theoretical physics and economics, as well as research workers in those areas, who want to enlarge their spectrum of knowledge towards the area of complexity and emergence. Since ideas and methods of the theory of complex systems also apply to other areas (from engineering and architecture to biology and medicine, e.g.), students and research workers from those areas will also profit from this book.

Presents highly interdisciplinary content Investigates deeply the theoretical foundations of complexity and emergence Summarizes the main challenges and open problems in several areas of science

Autorentext

Sergio Albeverio is a mathematician and mathematical physicist. Main research includes mathematical theory of Feynman path integrals, infinite dimensional Dirichlet forms, stochastic and p-adic, singular differential operators, asymptotics, non-standard analysis, algebra and number theory. Applications include quantum mechanics and field theory, astrophysics, biology, economics, urbanism and epistemology. Elisa Mastrogiacomo is Associate Professor at the Department of Economics of Insubria University. Her research covers stochastic analysis, stochastic differential equations, infinite dimensional analysis, control theory, set-valued analysis and financial mathematics. She is also interested in the dissemination of knowledge and use of learning to contribute to society's social, cultural and economic development (the University "third mission" or "extension activity"). Emanuela Rosazza Gianin is Professor of Mathematical Finance at Department of Statistics and Quantitative Methods at University of Milano-Bicocca, Italy. Her research interests focus on risk measures, BSDEs, option pricing and insurance premia. Stefania Ugolini is Assistant Professor of Probability at the Department of Mathematics at the University of Milan. She works in the area of probability and mathematical physics, with special attention to quantum mechanics and to symmetries and invariance properties of stochastic differential equations.

Inhalt

L. Boi, A topological and dynamical approach to the study of complex living systems.- I. Capelli, The complexity theory and financial systems regulation.- F. Guerra, The emergence of the order parameter in the interpolating replica trick for disordered statistical mechanics systems.- N. Ay, N. Bertschinger, J. Jost, E. Olbrich, J. Rauh, Information and complexity, or: where is the information?.- F. Patras and V. Planas-Bielsa, Complex systems: from the presocratics to pension funds.- F. Semboloni, From complex dynamics to the architecture of the city.- R. Seri, D. Secchi, M. Martinoli, Randomness, emergence and causation: a historical perspective of simulation in the social sciences.