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Features: New chapters on Barrier Options, Lookback Options, Asian
Options, Optimal Stopping Theorem, and Stochastic Volatility.
Contains over 235 exercises, and 16 problems with complete
solutions. Added over 150 graphs and figures, for more than 250 in
total, to optimize presentation. 57 R coding examples now
integrated into the book for implementation of the methods.
Substantially class-tested, so ideal for course use or self-study.
Stochastic analysis has a variety of applications to biological
systems as well as physical and engineering problems, and its
applications to finance and insurance have bloomed exponentially in
recent times. The goal of this book is to present a broad overview
of the range of applications of stochastic analysis and some of its
recent theoretical developments. This includes numerical
simulation, error analysis, parameter estimation, as well as
control and robustness properties for stochastic equations. The
book also covers the areas of backward stochastic differential
equations via the (non-linear) G-Brownian motion and the case of
jump processes. Concerning the applications to finance, many of the
articles deal with the valuation and hedging of credit risk in
various forms, and include recent results on markets with
transaction costs.
Stochastic analysis has a variety of applications to biological
systems as well as physical and engineering problems, and its
applications to finance and insurance have bloomed exponentially in
recent times. The goal of this book is to present a broad overview
of the range of applications of stochastic analysis and some of its
recent theoretical developments. This includes numerical
simulation, error analysis, parameter estimation, as well as
control and robustness properties for stochastic equations. The
book also covers the areas of backward stochastic differential
equations via the (non-linear) G-Brownian motion and the case of
jump processes. Concerning the applications to finance, many of the
articles deal with the valuation and hedging of credit risk in
various forms, and include recent results on markets with
transaction costs.
This monograph is an introduction to some aspects of stochastic
analysis in the framework of normal martingales, in both discrete
and continuous time. The text is mostly self-contained, except for
Section 5.7 that requires some background in geometry, and should
be accessible to graduate students and researchers having already
received a basic training in probability. Prereq- sites are mostly
limited to a knowledge of measure theory and probability,
namely?-algebras,expectations,andconditionalexpectations.Ashortint-
duction to stochastic calculus for continuous and jump processes is
given in Chapter 2 using normal martingales, whose predictable
quadratic variation is the Lebesgue measure. There already exists
several books devoted to stochastic analysis for c- tinuous
di?usion processes on Gaussian and Wiener spaces, cf. e.g. [51],
[63], [65], [72], [83], [84], [92], [128], [134], [143], [146],
[147]. The particular f- ture of this text is to simultaneously
consider continuous processes and jump processes in the uni?ed
framework of normal martingales.
This book provides an undergraduate-level introduction to discrete
and continuous-time Markov chains and their applications, with a
particular focus on the first step analysis technique and its
applications to average hitting times and ruin probabilities. It
also discusses classical topics such as recurrence and transience,
stationary and limiting distributions, as well as branching
processes. It first examines in detail two important examples
(gambling processes and random walks) before presenting the general
theory itself in the subsequent chapters. It also provides an
introduction to discrete-time martingales and their relation to
ruin probabilities and mean exit times, together with a chapter on
spatial Poisson processes. The concepts presented are illustrated
by examples, 138 exercises and 9 problems with their solutions.
Interest rate modeling and the pricing of related derivatives
remain subjects of increasing importance in financial mathematics
and risk management. This book provides an accessible introduction
to these topics by a step-by-step presentation of concepts with a
focus on explicit calculations. Each chapter is accompanied with
exercises and their complete solutions, making the book suitable
for advanced undergraduate and graduate level students.This second
edition retains the main features of the first edition while
incorporating a complete revision of the text as well as additional
exercises with their solutions, and a new introductory chapter on
credit risk. The stochastic interest rate models considered range
from standard short rate to forward rate models, with a treatment
of the pricing of related derivatives such as caps and swaptions
under forward measures. Some more advanced topics including the BGM
model and an approach to its calibration are also covered.
This book introduces the mathematics of stochastic interest rate
modeling and the pricing of related derivatives, based on a
step-by-step presentation of concepts with a focus on explicit
calculations. The types of interest rates considered range from
short rates to forward rates such as LIBOR and swap rates, which
are presented in the HJM and BGM frameworks. The pricing and
hedging of interest rate and fixed income derivatives such as bond
options, caps, and swaptions, are treated using forward measure
techniques. An introduction to default bond pricing and an outlook
on model calibration are also included as additional topics.This
third edition represents a significant update on the second edition
published by World Scientific in 2012. Most chapters have been
reorganized and largely rewritten with additional details and
supplementary solved exercises. New graphs and simulations based on
market data have been included, together with the corresponding R
codes.This new edition also contains 75 exercises and 4 problems
with detailed solutions, making it suitable for advanced
undergraduate and graduate level students.
This monograph is a progressive introduction to non-commutativity
in probability theory, summarizing and synthesizing recent results
about classical and quantum stochastic processes on Lie algebras.
In the early chapters, focus is placed on concrete examples of the
links between algebraic relations and the moments of probability
distributions. The subsequent chapters are more advanced and deal
with Wigner densities for non-commutative couples of random
variables, non-commutative stochastic processes with independent
increments (quantum Levy processes), and the quantum Malliavin
calculus. This book will appeal to advanced undergraduate and
graduate students interested in the relations between algebra,
probability, and quantum theory. It also addresses a more advanced
audience by covering other topics related to non-commutativity in
stochastic calculus, Levy processes, and the Malliavin calculus.
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