This textbook is an elementary introduction to the key topics in mathematical finance and financial economics - two realms of ideas that substantially overlap but are often treated separately from each other. Our goal is to present the highlights in the field, with the emphasis on the financial and economic content of the models, concepts and results. The book provides a novel, unified treatment of the subject by deriving each topic from common fundamental principles and showing the interrelations between the key themes. Although the presentation is fully rigorous, with some rare and clearly marked exceptions, the book restricts itself to the use of only elementary mathematical concepts and techniques. No advanced mathematics (such as stochastic calculus) is used.
Mean-Variance Portfolio Analysis: Portfolio Selection: Introductory Comments.- Mean-Variance Portfolio Analysis: The Markowitz Model.- Solution to the Markowitz Optimization Problem.- Properties of Efficient Portfolios.- The Markowitz Model with a Risk-Free Asset.- Efficient Portfolios in a Market with a Risk-Free Asset.- Capital Asset Pricing Model (CAPM).- CAPM Continued.- Factor Models and the Ross-Huberman APT.- Problems and Exercises I.- Derivative Securities Pricing: Dynamic Securities Market Model.- Risk-Neutral Pricing.- The Cox-Ross-Rubinstein Binomial Model.- American Derivative Securities.- From Binomial Model to Black-Scholes Formula.- Problems and Exercises II.- Growth and Equilibrium: Capital Growth Theory: Continued.- General Equilibrium Analysis of Financial Markets.- Behavioral Equilibrium and Evolutionary Dynamics.- Problems and Exercises III.- Mathematical Appendices: Facts from Linear Algebra.- Convexity and Optimization.- Sources.