Measure, Probability, and Mathematical Finance (PDF)

An introduction to the mathematical theory and financial
models developed and used on Wall Street

Providing both a theoretical and practical approach to the
underlying mathematical theory behind financial models, Measure,
Probability, and Mathematical Finance: A Problem-Oriented
Approach presents important concepts and results in measure
theory, probability theory, stochastic processes, and stochastic
calculus. Measure theory is indispensable to the rigorous
development of probability theory and is also necessary to properly
address martingale measures, the change of numeraire theory, and
LIBOR market models. In addition, probability theory is presented
to facilitate the development of stochastic processes, including
martingales and Brownian motions, while stochastic processes and
stochastic calculus are discussed to model asset prices and develop
derivative pricing models.

The authors promote a problem-solving approach when applying
mathematics in real-world situations, and readers are encouraged to
address theorems and problems with mathematical rigor. In addition,
Measure, Probability, and Mathematical Finance features:

* A comprehensive list of concepts and theorems from measure
theory, probability theory, stochastic processes, and stochastic
calculus

* Over 500 problems with hints and select solutions to reinforce
basic concepts and important theorems

* Classic derivative pricing models in mathematical finance that
have been developed and published since the seminal work of Black
and Scholes

Measure, Probability, and Mathematical Finance: A
Problem-Oriented Approach is an ideal textbook for introductory
quantitative courses in business, economics, and mathematical
finance at the upper-undergraduate and graduate levels. The book is
also a useful reference for readers who need to build their
mathematical skills in order to better understand the mathematical
theory of derivative pricing models.