The Brownian motion : a rigorous but gentle introduction for economists
Autor
Löffler, Andreas
Kruschwitz, Lutz
Institución
Resumen
The authors of this book are university professors in finance with many years of
experience in research and teaching. During these years, not only one but several
radical changes could be observed. During the period between 1960 and 1980, one
such thrust was that the research in the finance area was primarily characterized
by theoretical- and model-based analysis. Another thrust were the modern markets
such as the Chicago Board of Trade, which contributed to a significant increase in
the interest in the results of these theoretical research efforts. Also, the enormous
availability of data led to an extensive growth of empirical research in the field
with theoretical investigations taking a backseat. Furthermore, the interdisciplinary
orientation ensured that mathematicians also got enthusiastic about the subject
area and indeed strengthened the field. While this short overview of the scientific
development is undoubtedly incomplete, the concept of the Brownian motion always
played an important role.
There is no shortage of books providing a mathematical precise introduction of
this important concept. Similarly, the great deal of empirical research efforts have
analyzed the Brownian model. Furthermore, there exists an extensive literature for
practitioners looking for a first introduction to the Brownian motion. However, it is
our impression that in the rapid development, an important aspect of the Brownian
motion was lost. In particular, the relationship between mathematics and economics
did not receive the same level of attention. For our own courses, we were looking for
a textbook which could explain interested students in economics and finance what
mathematicians understand by a Brownian motion without these students having to
struggle with the deeper secrets of mathematics. We could not find such a book.
Therefore, we decided to write it ourselves. The reader is holding it in her hands.