Chapter 1
Introduction
Abstract This chapter sets the stage for the book when it establishes a common
theme in many physical and financial systems; both deal with dynamical systems
subject to external random forces. A brief discussion of the book’s target audience
follows, before an overview over its contents is given.
What do physics and finance have in common? The short answer is: they both deal
with dynamical systems that are subject to external random forces.
In physics, an example is the random walk of pollen floating on a liquid, the Brownian motion first interpreted and theoretically analyzed by Einstein [1]. A modern
example is the startup of conventional lasers and free-electron laser from noise. In
general, most of the sub-domain of statistical physics treats systems that are subject to random forces and are described by distributions of the state variables. Many
diffusion processes fall into this group.
In finance, the dynamics of the stocks or other financial quantities can often
be described by an average drift towards higher values that is superimposed by
large fluctuations. Bachelier’s analysis [2] was the first application of such random
processes to financial systems.
This correspondence was, of course, noted earlier and led to a large body of
literature, some under the name of Econophysics with notable books being [3–6].
The resemblance of the general features makes it possible to use similar mathematical
methods in order to describe and understand these systems. The target audience of
these volumes are mature physicists, eager to explore a new field.
In this book, however, we address students earlier in their career, typically in their
third or fourth year and use examples from finance to highlight concepts known from
physics with the intent to deepen their understanding of the methodology. Frequently,
we juxtapose systems from physics and systems from finance that use very similar
methods, albeit in different contexts. This approach should aid the students to see
methods from their physics education from a different angle, which should lead to
their increased appreciation. Seeing the same method applied to problems in rather
different contexts should deepen their understanding.
Moreover, some of the mathematical methods, such as stochastic differential equations or path integrals, are not part of the core curriculum. Presenting simple applications of these methods in two fields—physics and finance—side by side will fill
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
V. Ziemann, Physics and Finance, Undergraduate Lecture Notes in Physics,
https://doi.org/10.1007/978-3-030-63643-2_1
1
Introduction
Abstract This chapter sets the stage for the book when it establishes a common
theme in many physical and financial systems; both deal with dynamical systems
subject to external random forces. A brief discussion of the book’s target audience
follows, before an overview over its contents is given.
What do physics and finance have in common? The short answer is: they both deal
with dynamical systems that are subject to external random forces.
In physics, an example is the random walk of pollen floating on a liquid, the Brownian motion first interpreted and theoretically analyzed by Einstein [1]. A modern
example is the startup of conventional lasers and free-electron laser from noise. In
general, most of the sub-domain of statistical physics treats systems that are subject to random forces and are described by distributions of the state variables. Many
diffusion processes fall into this group.
In finance, the dynamics of the stocks or other financial quantities can often
be described by an average drift towards higher values that is superimposed by
large fluctuations. Bachelier’s analysis [2] was the first application of such random
processes to financial systems.
This correspondence was, of course, noted earlier and led to a large body of
literature, some under the name of Econophysics with notable books being [3–6].
The resemblance of the general features makes it possible to use similar mathematical
methods in order to describe and understand these systems. The target audience of
these volumes are mature physicists, eager to explore a new field.
In this book, however, we address students earlier in their career, typically in their
third or fourth year and use examples from finance to highlight concepts known from
physics with the intent to deepen their understanding of the methodology. Frequently,
we juxtapose systems from physics and systems from finance that use very similar
methods, albeit in different contexts. This approach should aid the students to see
methods from their physics education from a different angle, which should lead to
their increased appreciation. Seeing the same method applied to problems in rather
different contexts should deepen their understanding.
Moreover, some of the mathematical methods, such as stochastic differential equations or path integrals, are not part of the core curriculum. Presenting simple applications of these methods in two fields—physics and finance—side by side will fill
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
V. Ziemann, Physics and Finance, Undergraduate Lecture Notes in Physics,
https://doi.org/10.1007/978-3-030-63643-2_1
1