Preface
One fine day, my son, who was studying economics at the time, brought along
books on the use of stochastic differential equations in finance. Following a dialog
along the lines of “Oh, I know that, its a Fokker-Planck equation”—“No dad, that’s
Black-Scholes,” I got curious. After all, there might be some fun in economics and
finance, besides the money. So, I borrowed Hull’s book about the basics of financial
economics, because I wanted to understand the basic concepts and the lingo. Just
looking through the book, I recognized those differential equations that look so
similar to a diffusion equation with a drift term. So, I set out to understand what
finance has to do with diffusion.
I later presented some lectures about my explorations to a few interested students
and colleagues, which was very stimulating and caused me to explore the subject
further. That was how the later chapters came about. They all deal with some aspect
of random processes and have some overlap between physics, finance, and other
neighboring disciplines.
At that point, I prepared a 5 ECTS (European transfer credits) lecture series for
masters students at Uppsala University and expanded the manuscript to serve as
lecture notes for this course, which ran for the first time in the spring of 2019, with
about 15 interested students. The feedback after the course was rather positive such
that I gave the course again in the spring of 2020. This time with 24 students, who
provided much more feedback and criticism, which caused me to revise parts of the
manuscript to bring it to its present form.
Obviously, many people helped to improve the manuscript. First, I have to thank
my son Ingvar. He stimulated my interest in finance and also critically read parts
of the manuscript. Likewise, I am indebted to my colleagues and the students who
participated in the early lectures and in the course later. Many of them gave
valuable criticism and feedback on the growing manuscript. I want to single out a
few students, who were particularly diligent: Joe and Martin from the course in
2019; Friedrich, Sebastian, and Elias from 2020. They helped me weed out many
ambiguities and errors. They are, however, not to blame for any remaining bugs,
v
One fine day, my son, who was studying economics at the time, brought along
books on the use of stochastic differential equations in finance. Following a dialog
along the lines of “Oh, I know that, its a Fokker-Planck equation”—“No dad, that’s
Black-Scholes,” I got curious. After all, there might be some fun in economics and
finance, besides the money. So, I borrowed Hull’s book about the basics of financial
economics, because I wanted to understand the basic concepts and the lingo. Just
looking through the book, I recognized those differential equations that look so
similar to a diffusion equation with a drift term. So, I set out to understand what
finance has to do with diffusion.
I later presented some lectures about my explorations to a few interested students
and colleagues, which was very stimulating and caused me to explore the subject
further. That was how the later chapters came about. They all deal with some aspect
of random processes and have some overlap between physics, finance, and other
neighboring disciplines.
At that point, I prepared a 5 ECTS (European transfer credits) lecture series for
masters students at Uppsala University and expanded the manuscript to serve as
lecture notes for this course, which ran for the first time in the spring of 2019, with
about 15 interested students. The feedback after the course was rather positive such
that I gave the course again in the spring of 2020. This time with 24 students, who
provided much more feedback and criticism, which caused me to revise parts of the
manuscript to bring it to its present form.
Obviously, many people helped to improve the manuscript. First, I have to thank
my son Ingvar. He stimulated my interest in finance and also critically read parts
of the manuscript. Likewise, I am indebted to my colleagues and the students who
participated in the early lectures and in the course later. Many of them gave
valuable criticism and feedback on the growing manuscript. I want to single out a
few students, who were particularly diligent: Joe and Martin from the course in
2019; Friedrich, Sebastian, and Elias from 2020. They helped me weed out many
ambiguities and errors. They are, however, not to blame for any remaining bugs,
v