Stochastic Processes and Calculus

October 31, 2020
Stochastic Processes and Calculus

This textbook gives a comprehensive introduction to stochasticprocesses and calculus in the fields of finance and economics, morespecifically mathematical finance and time series econometrics.Over the past decades stochastic calculus and processes have gainedgreat importance, because they play a decisive role in the modelingof financial markets and as a basis for modern time serieseconometrics. Mathematical theory is applied to solve stochasticdifferential equations and to derive limiting results forstatistical 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 ofthe relevant topics without using many technical derivations. Onthe other hand many of the procedures are presented at atechnically advanced level: for a thorough understanding, they areto be proven. In order to meet both requirements jointly, thepresent book is equipped with a lot of challenging problems at theend of each chapter as well as with the corresponding detailedsolutions. Thus the virtual text - augmented with more than 60basic examples and 40 illustrative figures - is rather easy to readwhile a part of the technical arguments is transferred to theexercise problems and their solutions.