Description
Book SynopsisStochastic 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 conc
Trade Review'The text does a great job of providing a comprehensive picture of basic mathematical finance concepts in both discrete and continuous settings. The authors provide a balanced amount of details in both the financial (arbitrage, replicating strategies, etc.) and mathematical aspects (probability, stochastic calculus, etc.) I really appreciate the fact that the technical details are presented in a way that is accessible to an advanced undergraduate student.' Triet Pham, Department of Mathematics, The School of Arts and Sciences, Rutgers, The State University of New Jersey
'This is a rigorous textbook on stochastic finance in which the reader will enjoy the path the authors take while introducing conditional expectations with respect to sigma-algebras, and the sequence of models from the binomial to Black-Scholes. In all, a careful construction of the theory with proofs that are both thorough and readable.' Ludolf E. Meester, Delft University of Technology
Table of ContentsPreface; 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.
