Synopsis
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.
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