Optional Processes

<p>It is well-known that modern stochastic calculus has been exhaustively developed under usual 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.</p><p><strong><em>Optional Processes: Theory and Applications </em></strong>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.</p><p>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.</p><p>Features</p><ul> <p> </p> <li>Suitable for graduate students and researchers in mathematical finance actuarial science applied mathematics and related areas</li> </ul><ul> <p> </p> <li>Compiles almost all essential results on the calculus of optional processes in unusual probability spaces </li> <p> </p> <li>Contains many advanced analytical results for stochastic differential equations and statistics pertaining to the calculus of optional processes </li> <p> </p> <li>Develops new methods in finance based on optional processes such as a new portfolio theory defaultable claim pricing mechanism etc. </li> <p> </p> </ul>