Front cover; Preface to the second edition; Contents; Introduction; Chapter 1: Discrete-time models; Chapter 2: Optimal stopping problem and American options; Chapter 3: Brownian motion and stochastic di˙erentialequations; Chapter 4: The Black-Scholes model; Chapter 5: Option pricing and partial differential equations; Chapter 6: Interest rate models; Chapter 7: Asset models with jumps; Chapter 8: Credit risk models; Chapter 9: Simulation and algorithms for financial models; Appendix; Bibliography; Back cover
Summary
INTRODUCTION DISCRETE-TIME MODELS Discrete-time formalismMartingales and arbitrage opportunities Complete markets and option pricing Problem: Cox, Ross and Rubinstein model OPTIMAL STOPPING PROBLEM AND AMERICAN OPTIONS Stopping time The Snell envelope Decomposition of supermartingales Snell envelope and Markov chains Application to American options BROWNIAN MOTION AND STOCHASTIC DIFFERENTIAL EQUATIONS General comments on continuous-time processesBrownian motion Continuous-time martingales Stochastic integral and Itô calculus Stochastic differential equations THE BLACK-SCHOLES MODEL Description
