Stochastic Finance: An Introduction with Examples [Paperback]

A relaxed and user-friendly approach to understanding financial mathematics and the pricing of options with extensive examples and exercises.A relaxed and user-friendly introduction to financial mathematics for advanced undergraduate mathematics students. This is core material for students of financial mathematics, and fundamental for anyone planning a career in the field.A relaxed and user-friendly introduction to financial mathematics for advanced undergraduate mathematics students. This is core material for students of financial mathematics, and fundamental for anyone planning a career in the field.Stochastic Finance provides an introduction to mathematical finance that is unparalleled in its accessibility. Through classroom testing, the authors have identified common pain points for students, and their approach takes great care to help the reader to overcome these difficulties and to foster understanding where comparable texts often do not. Written for advanced undergraduate students, and making use of numerous detailed examples to illustrate key concepts, this text provides all the mathematical foundations necessary to model transactions in the world of finance. A first course in probability is the only necessary background. The book begins with the discrete binomial model and the finite market model, followed by the continuous BlackScholes model. It studies the pricing of European options by combining financial concepts such as arbitrage and self-financing trading strategies with probabilistic tools such as sigma algebras, martingales and stochastic integration. All these concepts are introduced in a relaxed and user-friendly fashion.Preface; Acknowledgements; Part I. Discrete-Time Models for Finance: 1. Introduction to finance; 2. Discrete probability; 3. Binomial or CRR model; 4. Finite market model; 5. Discrete BlackScholes model; Part II. Continuous-Time Models for Finance: 6. Continuous probability; 7. Brownian motion; 8. Stochastic integration; 9. The lsT