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This textbook gives a comprehensive introduction to stochastic
processes and calculus in the fields of finance and economics, more
specifically mathematical finance and time series econometrics.
Over the past decades stochastic calculus and processes have gained
great importance, because they play a decisive role in the modeling
of financial markets and as a basis for modern time series
econometrics. Mathematical theory is applied to solve stochastic
differential equations and to derive limiting results for
statistical inference on nonstationary processes. This introduction
is elementary and rigorous at the same time. On the one hand it
gives a basic and illustrative presentation of the relevant topics
without using many technical derivations. On the other hand many of
the procedures are presented at a technically advanced level: for a
thorough understanding, they are to be proven. In order to meet
both requirements jointly, the present book is equipped with a lot
of challenging problems at the end of each chapter as well as with
the corresponding detailed solutions. Thus the virtual text -
augmented with more than 60 basic examples and 40 illustrative
figures - is rather easy to read while a part of the technical
arguments is transferred to the exercise problems and their
solutions.
This textbook gives a comprehensive introduction to stochastic
processes and calculus in the fields of finance and economics, more
specifically mathematical finance and time series econometrics.
Over the past decades stochastic calculus and processes have gained
great importance, because they play a decisive role in the modeling
of financial markets and as a basis for modern time series
econometrics. Mathematical theory is applied to solve stochastic
differential equations and to derive limiting results for
statistical inference on nonstationary processes. This introduction
is elementary and rigorous at the same time. On the one hand it
gives a basic and illustrative presentation of the relevant topics
without using many technical derivations. On the other hand many of
the procedures are presented at a technically advanced level: for a
thorough understanding, they are to be proven. In order to meet
both requirements jointly, the present book is equipped with a lot
of challenging problems at the end of each chapter as well as with
the corresponding detailed solutions. Thus the virtual text -
augmented with more than 60 basic examples and 40 illustrative
figures - is rather easy to read while a part of the technical
arguments is transferred to the exercise problems and their
solutions.
This book presents modern developments in time series econometrics
that are applied to macroeconomic and financial time series,
bridging the gap between methods and realistic applications. It
presents the most important approaches to the analysis of time
series, which may be stationary or nonstationary. Modelling and
forecasting univariate time series is the starting point. For
multiple stationary time series, Granger causality tests and vector
autogressive models are presented. As the modelling of
nonstationary uni- or multivariate time series is most important
for real applied work, unit root and cointegration analysis as well
as vector error correction models are a central topic. Tools for
analysing nonstationary data are then transferred to the panel
framework. Modelling the (multivariate) volatility of financial
time series with autogressive conditional heteroskedastic models is
also treated.
This book presents modern developments in time series econometrics
that are applied to macroeconomic and financial time series,
bridging the gap between methods and realistic applications. It
presents the most important approaches to the analysis of time
series, which may be stationary or nonstationary. Modelling and
forecasting univariate time series is the starting point. For
multiple stationary time series, Granger causality tests and vector
autogressive models are presented. As the modelling of
nonstationary uni- or multivariate time series is most important
for real applied work, unit root and cointegration analysis as well
as vector error correction models are a central topic. Tools for
analysing nonstationary data are then transferred to the panel
framework. Modelling the (multivariate) volatility of financial
time series with autogressive conditional heteroskedastic models is
also treated.
Stochastische Integralrechnung und Zeitreihenmodellierung spielen
fur Wirtschaftswissenschaftler eine entscheidende Rolle bei der
Modellierung von Finanzmarkten und fur die statistische Inferenz
instationarer Zeitreihen. Diese elementare und zugleich rigorose
Einfuhrung betrachtet beide Gebiete. Leser lernen so die modernen
Methoden der mathematischen Finanzierungstheorie und der
Zeitreihenoekonometrie kennen. Der Autor verzichtet weitestgehend
auf mathematische Ableitungen und stellt die Konzepte und Techniken
anhand anschaulicher Beispiele vor. Am Ende eines jeden Kapitels
finden sich uber 100 Probleme und UEbungsaufgaben samt kompletter
Loesung, welche technische Details und Beweise enthalten und so ein
hohes formales Niveau garantieren.
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