Financial mathematics refers to the application of mathematical methods and models to financial concerns. It uses techniques from statistics, economic theory, probability, and stochastic processes. The application of mathematics to the financial sector is based on several financial or economic hypotheses. It employs abstract mathematical methods in order to build mathematical models of the functioning of financial mechanisms. Mathematics is also used in economics for building economic models that utilize mathematical methods and principles for analyzing economic problems. In economics, mathematics is used to conduct quantitative experiments and develop models for forecasting future economic growth. Mathematical economics is based on modern data methods, computing models, and other advanced mathematical applications. This book unravels the recent studies in the field of mathematical finance and mathematical economics. Most of the topics introduced herein cover new methods and modeling techniques used in mathematical finance and mathematical economics. The book will serve as a valuable source of reference for graduate and postgraduate students.