Stochastic Finance An Introduction with Examples

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 Black?Scholes 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 Black–Scholes model; Part II. Continuous-Time Models for Finance: 6. Continuous probability; 7. Brownian motion; 8. Stochastic integration; 9. The Black–Scholes model; A Supplementary material; Bibliography; Symbol index; Index.

Amanda Turner is Professor of Statistics at the University of Leeds. She received her Ph.D. from the University of Cambridge in Scaling Limits of Stochastic Processes in 2007. Before moving to Leeds, she taught probability and stochastic processes for finance at Lancaster University and the University of Geneva for over fifteen years. She is a founding member of the Royal Statistical Society's Applied Probability Section and is heavily involved in the London Mathematical Society, including as a member of council since 2021. When not doing mathematics, she enjoys mountaineering and skiing.
Dirk Zeindler is Senior Lecturer in Pure Mathematics at Lancaster University. He holds a Ph.D. in random matrix theory from the University of Zurich. He has taught probability courses at Lancaster University and at the University of Bielefeld for over ten years. His teaching includes introductory first-year probability to advanced financial mathematics, for mathematics, accounting and finance students. His research interests are in probability and number theory. In particular, he and his co-authors have proven that at least 41.7% of the zeros of the Riemann zeta lie on the critical line, which is the current world record.