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