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This sequel to Brownian Motion and Stochastic Calculus by the same
authors develops contingent claim pricing and optimal
consumption/investment in both complete and incomplete markets,
within the context of Brownian-motion-driven asset prices. The
latter topic is extended to a study of equilibrium, providing
conditions for existence and uniqueness of market prices which
support trading by several heterogeneous agents. Although much of
the incomplete-market material is available in research papers,
these topics are treated for the first time in a unified manner.
The book contains an extensive set of references and notes
describing the field, including topics not treated in the book.
This book will be of interest to researchers wishing to see
advanced mathematics applied to finance. The material on optimal
consumption and investment, leading to equilibrium, is addressed to
the theoretical finance community. The chapters on contingent claim
valuation present techniques of practical importance, especially
for pricing exotic options.
In the last twenty years extensive research has been devoted to a
better understanding of the stable and other closely related
infinitely divisible mod els. Stamatis Cambanis, a distinguished
educator and researcher, played a special leadership role in the
development of these research efforts, particu larly related to
stable processes from the early seventies until his untimely death
in April '95. This commemorative volume consists of a collection of
research articles devoted to reviewing the state of the art of this
and other rapidly developing research and to explore new directions
of research in these fields. The volume is a tribute to the Life
and Work of Stamatis by his students, friends, and colleagues whose
personal and professional lives he has deeply touched through his
generous insights and dedication to his profession. Before the idea
of this volume was conceived, two conferences were held in the
memory of Stamatis. The first was organized by the University of
Athens and the Athens University of Economics and was held in
Athens during December 18-19, 1995. The second was a significant
part of a Spe cial IMS meeting held at the campus of the University
of North Carolina at Chapel Hill during October 17-19, 1996. It is
the selfless effort of sev eral people that brought about these
conferences. We believe that this is an appropriate place to
acknowledge their effort; and on behalf of all the participants, we
extend sincere thanks to all these persons."
A graduate-course text, written for readers familiar with measure-theoretic probability and discrete-time processes, wishing to explore stochastic processes in continuous time. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a martingale and a Markov process with continuous paths. In this context, the theory of stochastic integration and stochastic calculus is developed, illustrated by results concerning representations of martingales and change of measure on Wiener space, which in turn permit a presentation of recent advances in financial economics. The book contains a detailed discussion of weak and strong solutions of stochastic differential equations and a study of local time for semimartingales, with special emphasis on the theory of Brownian local time. The whole is backed by a large number of problems and exercises.
This volume contains papers presented during a four-day Workshop
that took place at Rutgers University from 29 April to 2 May, 1991.
The purpose of this workshop was to promote interaction among
specialists in these areas byproviding for all an up-to-date
picture of current issues and outstanding problems. The topics
covered include singular stochasticcontrol, queuing networks, the
mathematical theory of stochastic optimization and filtering,
adaptive control and the estimation for random fields and its
connections with simulated annealing, statistical mechanics, and
combinatorial optimization.
There has been extensive research in the past twenty years devoted
to a better understanding of the stable and other closely related
infinitely divisible models. The late Professor Stamatis Cambanis,
a distinguished educator and researcher, played a special
leadership role in the development of these fields from the early
seventies until his untimely death in April 1995. This
commemorative volume honoring Stamatis Cambanis consists of a
collection of research articles devoted to review the state of the
art in rapidly developing research areas in Stochastic Processes
and to explore new directions of research. The volume is a tribute
to the life and work of Stamatis by his students, friends, and
colleagues whose personal and professional lives he deeply touched
through his generous insights and dedication to his profession.
This book develops a mathematical theory for finance, based on a
simple and intuitive absence-of-arbitrage principle. This posits
that it should not be possible to fund a non-trivial liability,
starting with initial capital arbitrarily near zero. The principle
is easy-to-test in specific models, as it is described in terms of
the underlying market characteristics; it is shown to be equivalent
to the existence of the so-called ""Kelly"" or growth-optimal
portfolio, of the log-optimal portfolio, and of appropriate local
martingale deflators. The resulting theory is powerful enough to
treat in great generality the fundamental questions of hedging,
valuation, and portfolio optimization. The book contains a
considerable amount of new research and results, as well as a
significant number of exercises. It can be used as a basic text for
graduate courses in Probability and Stochastic Analysis, and in
Mathematical Finance. No prior familiarity with finance is
required, but it is assumed that readers have a good working
knowledge of real analysis, measure theory, and of basic
probability theory. Familiarity with stochastic analysis is also
assumed, as is integration with respect to continuous
semimartingales.
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