Measure, Probability, and Mathematical Finance

An introduction to the mathematical theory and financialmodels developed and used on Wall Street Providing both a theoretical and practical approach to theunderlying mathematical theory behind financial models, Measure,Probability, and Mathematical Finance: A Problem-OrientedApproach presents important concepts and results in measuretheory, probability theory, stochastic processes, and stochasticcalculus. Measure theory is indispensable to the rigorousdevelopment of probability theory and is also necessary to properlyaddress martingale measures, the change of numeraire theory, andLIBOR market models. In addition, probability theory is presentedto facilitate the development of stochastic processes, includingmartingales and Brownian motions, while stochastic processes andstochastic calculus are discussed to model asset prices and developderivative pricing models. The authors promote a problem-solving approach when applyingmathematics in real-world situations, and readers are encouraged toaddress theorems and problems with mathematical rigor. In addition,Measure, Probability, and Mathematical Finance features: * A comprehensive list of concepts and theorems from measuretheory, probability theory, stochastic processes, and stochasticcalculus * Over 500 problems with hints and select solutions to reinforcebasic concepts and important theorems * Classic derivative pricing models in mathematical finance thathave been developed and published since the seminal work of Blackand Scholes Measure, Probability, and Mathematical Finance: AProblem-Oriented Approach is an ideal textbook for introductoryquantitative courses in business, economics, and mathematicalfinance at the upper-undergraduate and graduate levels. The book isalso a useful reference for readers who need to build theirmathematical skills in order to better understand the mathematicaltheory of derivative pricing models.