Optional processes: theory and applications

By:

Abdelghani, Mohamed

Contributor(s):

Melnikov, Alexander

Material type: Text

TextSeries: Chapman & Hall/CRC Financial Mathematics SeriesPublication details: CRC Press Boca Raton 2020Description: xiii, 378 pISBN:

9780367508517

Subject(s):

Stochastic calculus

DDC classification:

519.23 ABD

Summary: 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. 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)

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Holdings
Item type	Current library	Collection	Call number	Copy number	Status	Date due	Barcode
Book	Indian Institute of Management LRC General Stacks	Operations Management & Quantitative Techniques	519.23 ABD (Browse shelf(Opens below))	1	Available		006656

Table 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]

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.

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)

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