Measure, Probability, and Mathematical Finance

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 

GUOJUN GAN, PHD, ASA, is Director of Quantitative Modeling and Model Efficiency at Manulife Financial, Canada. His research interests include empirical corporate finance, actuarial science, risk management, data mining, and big data analysis.

CHAOQUN MA, PHD, is Professor and Dean of the School of Business Administration at Hunan University, China. The recipient of First Prize in Outstanding Achievements in Teaching in 2009, Dr. Ma’s research interests include financial engineering, risk management, and data mining.

HONG XIE, PHD, is Adjunct Professor in the Department of Mathematics and Statistics at York University as well as Vice President of Models and Analytics at Manulife Financial, Canada. Dr. Xie is on the Board of Directors for the Canadian-Chinese Finance Association, and his research interests include financial engineering, mathematical finance, and partial differential equations.