Nonlinear Problems: Mathematical Modeling, Analyzing, and Computing for Finance

Modern financial markets encapsulate vast number of interconnected financial entities, instruments, and strategies. Understanding these complex dynamical systems requires multidisciplinary efforts from a wide range of quantitative fields including mathematics, statistics, data mining, and operations research. While conventional financial research focuses mostly on linear models of variables of interest, they cannot copewith real-world financial phenomena. In the past decade, we have seen significant progress in our fundamental understanding of dynamical financial and economic behaviors, both from the microand macroprospectives, using nonlinear systems and methodologies. Powerful techniques borrowed from traditional nonlinear models and new methods invented have been brought to almost every aspect of financial research, including asset pricing, risk management, and financial forecasting. Still, there exist many challenging problems. In spite of the amount of published results recently focused on dynamical financial and economic behaviors, there remain many challenging open questions. The aim of this special issue is to gather recent research efforts on the development and applications of nonlinear techniques to address the critical issues in finance and to see the latest developments. The original papers explored in this special issue include a wide variety of topics such as the following.