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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.
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.
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