Portfolio Choice
Introduction
Utility
Mean-variance analysis
The Binomial Model
One-period model
Multi-period model
A General Discrete-Time Model
One-period model
Multi-period model
Brownian Motion
Introduction
Hitting-time distributions
Girsanov’s theorem
Brownian motion as a limit
Stochastic calculus
The Black–Scholes Model
Introduction
The Black–Scholes formula
Hedging and the Black–Scholes equation
Path-dependent claims
Dividend-paying assets
Interest-Rate Models
Introduction
Survey of interest-rate models
Gaussian random-field model
Appendix A: Mathematical Preliminaries
Appendix B: Solutions to the Exercises
Further Reading
References
Index
Exercises appear at the end of each chapter.
Biography
Douglas Kennedy is a Fellow of Trinity College in Cambridge, UK.
[T]he author covers a number of topics which are normally not addressed in introductions to stochastic finance, and he takes a new and innovative road in the derivation of many familiar results. … the book does contain a lot of interesting material (some of it non-standard) that can enrich a lecture course and deepen the reader’s understanding of financial mathematics, so that it definitely belongs on the shelf of every serious student/teacher in the field. …
All notions and concepts are defined and well explained. … Specific calculations of any type are included on almost any page and it is clear how important this is for a good understanding of the material. … this well-written book prepared by a well-experienced teacher and researcher will be met with interest by many readers. The wide range of topics discussed in detail makes the book appropriate for courses in financial mathematics at both undergraduate and graduate levels.
—Ruediger Frey, The American Statistician, August 2011
—Journal of the Royal Statistical Society, Series A, April 2011This book is a superb beginning level text for senior undergraduate/graduate mathematicians, which is based on lectures delivered by its author to many generations of appreciative Cambridge mathematicians. Many of my own Ph.D. and masters students have taken Dr. Kennedy’s course to uniformly good reviews; this readable book will make its material available to a worldwide audience. I have in the past struggled with some of Dr. Kennedy’s exercises, but the book contains 40 pages of fully worked out solutions to help introduce the reader to the Oxbridge style of learning by problem solving in which even supervisors are sometimes challenged.
—M.A.H. Dempster, Centre for Financial Research, Statistical Laboratory, University of Cambridge, UK
