Measure, Probability, And Mathematical Finance: A Problem-Oriented Approach

This book is organized into five parts, each of which is further organized into several chapters. The five parts are: Part One, Measure Theory; Part Two, Probability Theory, Part Three, Stochastic Processes; Part Four, Stochastic Calculus, and Part Five, Stochastic Financial Models. Measure theory is indispensable to the rigorous to the development of probability theory and is also necessary to properly address martingale measures, the change of numeraire theory, and the LIBOR market models. Probability theory is presented to facilitate the development of stochastic processes, including martingales and Brownian motions. In addition, stochastic processes and calculus are discussed due to their importance to modern mathematical finance since they are vital to model asset prices and the development of derivative pricing models. Each chapter is divided into five sections: the first section presents the definitions of important concepts and theorems; the second, third, and fourth sections present hints about how to solve the problems as well as the full solutions of the problems; and the fifth section contains detailed bibliographical notes.

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.