David M. Kreps is the Adams Distinguished Professor of Management, Emeritus at the Graduate School of Business, Stanford University, California. He has been honored with many awards, including the John Bates Clark Medal by the American Economic Association in 1989 and the Carty Prize for the Advancement of Science by the National Academy of Sciences in 2018.

'He did it again - David M. Kreps, the unparalleled master of theory and exposition, now adds detailed discrete underpinnings to the Black-Scholes-Merton model. This beautifully written monograph forms bookends with the foundational Harrison-Kreps martingale theory of financial asset pricing. Every researcher and student in this field will want a copy!' Darrell Duffie, Dean Witter Distinguished Professor of Finance, Stanford University, California

• 1. Introduction; 2. Finitely many states and dates; 3. Countinuous time and the Black-Scholes-Merton (BSM) Model; 4. BSM as an idealization of binomial-random-walk economies; 5. Random walks that are not binomial; 6. Barlow's example; 7. The Pötzelberger-Schlumprecht example and asymptotic arbitrage; 8. Concluding remarks, Part I: how robust an idealization is BSM?; 9. Concluding remarks, Part II: continuous-time models as idealizations of discrete time; Appendix.

David M. Kreps is the Adams Distinguished Professor of Management, Emeritus at the Graduate School of Business, Stanford University, California. He has been honored with many awards, including the John Bates Clark Medal by the American Economic Association in 1989 and the Carty Prize for the Advancement of Science by the National Academy of Sciences in 2018.

'He did it again - David M. Kreps, the unparalleled master of theory and exposition, now adds detailed discrete underpinnings to the Black-Scholes-Merton model. This beautifully written monograph forms bookends with the foundational Harrison-Kreps martingale theory of financial asset pricing. Every researcher and student in this field will want a copy!' Darrell Duffie, Dean Witter Distinguished Professor of Finance, Stanford University, California

• 1. Introduction; 2. Finitely many states and dates; 3. Countinuous time and the Black-Scholes-Merton (BSM) Model; 4. BSM as an idealization of binomial-random-walk economies; 5. Random walks that are not binomial; 6. Barlow's example; 7. The Pötzelberger-Schlumprecht example and asymptotic arbitrage; 8. Concluding remarks, Part I: how robust an idealization is BSM?; 9. Concluding remarks, Part II: continuous-time models as idealizations of discrete time; Appendix.