Filling the void between surveys of the field with relatively
light mathematical content and books with a rigorous, formal
approach to stochastic integration and probabilistic ideas,
Stochastic Financial Models provides a sound introduction to
mathematical finance. The author takes a classical applied
mathematical approach, focusing on calculations rather than seeking
the greatest generality.
Developed from the esteemed author's advanced undergraduate and
graduate courses at the University of Cambridge, the text begins
with the classical topics of utility and the mean-variance approach
to portfolio choice. The remainder of the book deals with
derivative pricing. The author fully explains the binomial model
since it is central to understanding the pricing of derivatives by
self-financing hedging portfolios. He then discusses the general
discrete-time model, Brownian motion and the Black?Scholes model.
The book concludes with a look at various interest-rate models.
Concepts from measure-theoretic probability and solutions to the
end-of-chapter exercises are provided in the appendices.
By exploring the important and exciting application area of
mathematical finance, this text encourages students to learn more
about probability, martingales and stochastic integration. It shows
how mathematical concepts, such as the Black?Scholes and Gaussian
random-field models, are used in financial situations.
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