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. Read more...
Abstract:
Suitable for students of mathematical finance, or a quick introduction to researchers and finance practitioners. This book covers the stochastic calculus theory required, as well as many key finance topics, including a chapter dedicated to credit risk modeling. Read more...
Author(s): Lamberton, Damien; Lapeyre, Bernard
Series: Chapman & Hall/CRC financial mathematics series
Edition: 2nd ed
Publisher: CRC Press
Year: 2011
Language: English
Pages: 253
City: Hoboken
Tags: Финансово-экономические дисциплины;Финансовая математика;
Content: 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
