Mathematical techniques in finance : an introduction

"Finance as a distinct field from economics is generally defined as the science or study of the management of funds. The creation of credit, savings, investments, banking institutions, financial markets and products, risk management all fall under the purview of finance. The unifying themes in finance are time, risk and money. Mathematical or quantitative finance is the application of mathematics to these core areas. While simple arithmetic was enough for accounting and keeping ledgers and double-entry bookkeeping, Louis Bachelier's doctoral thesis, Theorie de la speculation published in 1900 used Brownian motion to study stock prices, and is widely recognized as the beginning of quantitative finance. Since then, the use of increasingly sophisticated and specialized mathematics has created the modern field of quantitative finance encompassing investment theory, asset pricing, derivatives, financial data science and the emerging area of crypto assets and Decentralized Finance (DeFi)"--