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Stochastic Analysis for Finance with Simulations
This book is an introduction to stochastic analysis and quantitative finance, including theoretical and computational methods, for advanced undergraduate and graduate students in mathematics and business, but not excluding practitioners in finance
industry. The book is designed for readers who want to have a deeper understanding
of the delicate theory of quantitative finance by doing computer simulations in
addition to theoretical study. Topics include stochastic calculus, option pricing,
optimal portfolio investment, and interest rate models. Also included are simulations of stochastic phenomena, numerical solutions of the Black–Scholes–Merton
equation, Monte Carlo methods, and time series. Basic measure theory is used as a
tool to describe probabilistic phenomena. The level of familiarity with computer
programming is kept to a minimum. To make the book accessible to a wider
audience, some background mathematical facts are included in the first part of the
book and also in the appendices.
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