Chapter 1 - Preliminaries and Review

Abstract

Chapter 1 provides a concise review of essential prerequisite material for financial mathematics along with brief discussions of financial securities and markets. The securities and markets sections introduce equity, fixed income, and derivatives instruments along with the markets in which they trade along with essential financial practices such as arbitrage and short selling. Mathematics reviews include matrix arithmetic, vector spaces and span, differential and integral calculus, all illustrated with relevant examples drawn from finance. Matrices are applied to solving systems of equations. Taylor series and LaGrange optimization are discussed along with differentials and Riemann sums. All of these topics are reviewed with the goal of applying their principles to understanding discrete and continuous valuation, basic stochastic calculus, and their applications to valuing and managing equity, fixed income, and derivative instruments.