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Introduction to the Mathematics of Finance: Arbitrage and Option Pricing

Table of Contents

Preface.- Notation Key and Greek Alphabet.- 0 Introduction.- Part 1 Options and Arbitrage.- 1 Background on Options.- 2 An Aperitif on Arbitrage.- Part 2 Discrete-Time Pricing Models.- 3 Discrete Probability.- 4 Stochastic Processes, Filtrations and Martingales.- 5 Discrete-Time Pricing Models.- 6 The Binomial Model.- 7 Pricing Nonattainable Alternatives in an Incomplete Market.- 8 Optimal Stopping and American Options.- Part 3 the Black-Scholes Option Pricing Formula.- 9 Continuous Probability.- 10 The Black-Scholes Option Pricing Formula.- Appendix A: Convexity and the Separation Theorem.- Appendix B: Closed, Convex Cones.- Selected Solutions.- References.- Index

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