The Brownian motion : a rigorous but gentle introduction for economists

Abstract

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.