An Elementary Introduction to Mathematical Finance

Sheldon M. Ross is the Epstein Chair Professor at the Department of Industrial and Systems Engineering, University of Southern California. He received his Ph.D. in statistics at Stanford University in 1968 and was formerly a Professor at the University of California, Berkeley, from 1976 until 2004. He has published more than 100 articles and a variety of textbooks in the areas of statistics and applied probability, including Topics in Finite and Discrete Mathematics (2000), Introduction to Probability and Statistics for Engineers and Scientists, 4th edition (2009), A First Course in Probability, 8th edition (2009), and Introduction to Probability Models, 10th edition (2009), among others. Dr Ross serves as the editor for Probability in the Engineering and Informational Sciences.

1. Probability; 2. Normal random variables; 3. Geometric Brownian motion; 4. Interest rates and present value analysis; 5. Pricing contracts via arbitrage; 6. The Arbitrage Theorem; 7. The Black–Scholes formula; 8. Additional results on options; 9. Valuing by expected utility; 10. Stochastic order relations; 11. Optimization models; 12. Stochastic dynamic programming; 13. Exotic options; 14. Beyond geometric motion models; 15. Autoregressive models and mean reversion.