Mathematical finance refers to a branch of applied mathematics concerned with the application of mathematics and mathematical modeling for solving financial problems and modeling financial markets. It is also known as quantitative finance and financial mathematics. The field combines tools from probability, statistics and stochastic processes with economic theory. There are various applications of mathematical finance, including risk management, data mining, stock trading, econometrics, forecasting, inventory management, marketing, and investing strategies. Risk management is one of the major applications of mathematical finance that helps in the identification and management of financial risks. Mathematical finance is used to mine financial data, which helps to manage financial risks and reduce expenses by recognizing the anomalies and patterns in data. It is used across several industries, such as manufacturing, banking, retail and technology for making predictions based on data. This book traces the progress of mathematical finance and highlights some of its key theories, tools and applications. It aims to present researches that have transformed this discipline and aided its advancement. With state-of-the-art inputs by acclaimed experts of this field, this book targets students and professionals.