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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.
This book focuses on the application of the partial hedging
approach from modern math finance to equity-linked life insurance
contracts. It provides an accessible, up-to-date introduction to
quantifying financial and insurance risks. The book also explains
how to price innovative financial and insurance products from
partial hedging perspectives. Each chapter presents the problem,
the mathematical formulation, theoretical results, derivation
details, numerical illustrations, and references to further
reading.
This book focuses on the application of the partial hedging
approach from modern math finance to equity-linked life insurance
contracts. It provides an accessible, up-to-date introduction to
quantifying financial and insurance risks. The book also explains
how to price innovative financial and insurance products from
partial hedging perspectives. Each chapter presents the problem,
the mathematical formulation, theoretical results, derivation
details, numerical illustrations, and references to further
reading.
Risk Analysis in Finance and Insurance, Second Edition presents an
accessible yet comprehensive introduction to the main concepts and
methods that transform risk management into a quantitative science.
Taking into account the interdisciplinary nature of risk analysis,
the author discusses many important ideas from mathematics,
finance, and actuarial science in a simplified manner. He explores
the interconnections among these disciplines and encourages readers
toward further study of the subject. This edition continues to
study risks associated with financial and insurance contracts,
using an approach that estimates the value of future payments based
on current financial, insurance, and other information. New to the
Second Edition Expanded section on the foundations of probability
and stochastic analysis Coverage of new topics, including financial
markets with stochastic volatility, risk measures, risk-adjusted
performance measures, and equity-linked insurance More worked
examples and problems Reorganized and expanded, this updated book
illustrates how to use quantitative methods of stochastic analysis
in modern financial mathematics. These methods can be naturally
extended and applied in actuarial science, thus leading to unified
methods of risk analysis and management.
Risk Analysis in Finance and Insurance, Second Edition presents an
accessible yet comprehensive introduction to the main concepts and
methods that transform risk management into a quantitative science.
Taking into account the interdisciplinary nature of risk analysis,
the author discusses many important ideas from mathematics,
finance, and actuarial science in a simplified manner. He explores
the interconnections among these disciplines and encourages readers
toward further study of the subject. This edition continues to
study risks associated with financial and insurance contracts,
using an approach that estimates the value of future payments based
on current financial, insurance, and other information. New to the
Second Edition Expanded section on the foundations of probability
and stochastic analysis Coverage of new topics, including financial
markets with stochastic volatility, risk measures, risk-adjusted
performance measures, and equity-linked insurance More worked
examples and problems Reorganized and expanded, this updated book
illustrates how to use quantitative methods of stochastic analysis
in modern financial mathematics. These methods can be naturally
extended and applied in actuarial science, thus leading to unified
methods of risk analysis and management.
This Festschrift is published in honor of Rodney G. Downey, eminent
logician and computer scientist, surfer and Scottish country
dancer, on the occasion of his 60th birthday. The Festschrift
contains papers and laudations that showcase the broad and
important scientific, leadership and mentoring contributions made
by Rod during his distinguished career. The volume contains 42
papers presenting original unpublished research, or expository and
survey results in Turing degrees, computably enumerable sets,
computable algebra, computable model theory, algorithmic
randomness, reverse mathematics, and parameterized complexity, all
areas in which Rod Downey has had significant interests and
influence. The volume contains several surveys that make the
various areas accessible to non-specialists while also including
some proofs that illustrate the flavor of the fields.
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