000			02715nam a22002177a 4500
005			20241129185643.0
008			241129b |||||||| |||| 00| 0 eng d
020			_a9780367508517
082			_a519.23 _bABD
100			_aAbdelghani, Mohamed _919130
245			_aOptional processes: _btheory and applications
260			_bCRC Press _aBoca Raton _c2020
300			_axiii, 378 p.
365			_aGBP _b45.99
490			_aChapman & Hall/CRC Financial Mathematics Series
500			_aTable of content: 1. Spaces, Laws and Limits. 2. Stochastic Processes. 3. Martingales. 4. Strong Supermartingales. 5. Optional Martingales. 6. Optional Supermartingales Decomposition. 7. Calculus of Optional Semimartingales. 8. Optional Stochastic Equations. 9. Optional Financial Markets. 10. Defaultable Markets on Unusual Space. 11. Filtering of Optional Semimartingales. Bibliography. Index. [https://www.routledge.com/Optional-Processes-Theory-and-Applications/Abdelghani-Melnikov/p/book/9780367508517]
520			_aIt 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. Optional Processes: Theory and Applications 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. Features Suitable for graduate students and researchers in mathematical finance, actuarial science, applied mathematics and related areas Compiles 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. (https://www.routledge.com/Optional-Processes-Theory-and-Applications/Abdelghani-Melnikov/p/book/9780367508517)
650			_aStochastic calculus _919131
700			_aMelnikov, Alexander _919132
942			_cBK _2ddc
999			_c7767 _d7767