Market-Consistent Prices

Pablo Koch-Medina is Professor of Finance and Insurance at the University of Zurich and Director of the Center for Finance and Insurance at the same university. He studied mathematics at the Universities of Leiden and Zurich and holds a PhD in mathematics from the University of Zurich.   Cosimo Munari is Professor of Finance and Insurance at the University of Zurich. He studied mathematics at the University of Milan and Finance at Collegio Carlo Alberto in Turin and holds a PhD in mathematics from the Swiss Federal Institute of Technology in Zurich.

• Introduction.- A full picture in the simplest case.- Part I: One-period models.- Finite probability spaces.-Random variables.- The space of random variables.- Separation theorems.- Positive linear functionals.- One-period models: The Law of One Price.- One-period models: The Fundamental Theorem of Asset Pricing.- One-period models: Incomplete markets.- Part II: Multi-period models.- Information and measurability.-Conditional probabilities and conditional expectation.- Stochastic processes and martingales.- Multi-period models: The Law of One Price.- Multi-period models: The Fundamental Theorem of Asset Pricing.- Multi-period models: Incomplete markets.- The Cox-Ross-Rubinstein model.- Optimal stopping.- Multi-period models: American claims.- Part III: The Black-Scholes formula.- The central limit theorem.- The Black-Scholes formula.- Appendices.- A  Linear algebra.- B  Normed spaces.- C. Combinatorics.