Optional Processes：Theory and Applications

It is well-known that modern stochastic calculus has been exhaustively developed under standard conditions. Despite such a well-developed theory, there is evidence to suggest that these very convenient technical conditions cannot necessarily be fulfilled in real-world applications. Optional Processes: Theory and Applications is a book that seeks to delve into the existing theory, new developments and applications of optional processes on "unusual" probability spaces.

The development of stochastic calculus of optional processes marks the beginning of a new and more general form of stochastic analysis. This book aims to provide an accessible, comprehensive and up-to-date exposition of optional processes and their numerous properties. Furthermore, the book presents not only current theory of optional processes, but it also contains a spectrum of applications to stochastic differential equations, filtering theory and mathematical finance.

FeaturesSuitable for graduate students and researchers in mathematical finance, actuarial science, applied mathematics and related areasCompiles almost all essential results on the calculus of optional processes in unusual probability spaces Contains many advanced analytical results for stochastic differential equations and statistics pertaining to the calculus of optional processes Develops new methods in finance based on optional processes such as a new portfolio theory, defaultable claim pricing mechanism etc.