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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