Applications of state space models in finance

Notation and conventions
The outline throughout this thesis relies on notation and conventions that are in common
use. The numerous mathematical symbols introduced in the theoretical part of this
thesis are based on the standard Greek and English alphabets. As a consequence, the
same symbol might have different connotations. By defining all employed symbols and
abbreviations in the text, the different meaning should generally become obvious from
the context. The following notation and conventions are adopted:
Vectors, denoted by lower-case letters, and matrices, denoted by upper-case letters,
are printed in bold type.
If a vector x is identically and independently distributed (IID) with mean µ and
variance matrix H, we write x ∼ IID(µ, H).
The expression “log” generally refers to the natural logarithm.
Phrases printed in italics are particularly important in the context of the respective
section.
Expressions either referring to software packages, to web links or to mnemonics
are printed in typewriter style.
In connection with the use of trade and service marks, the ¡
and
placed in the top right-hand corner of the mark, respectively.
symbols are
Throughout this thesis, the symbol “ ¢ ” is used as a reference to a chapter, a section
or a subsection.
In the list of references, any links to the internet are given together with their
respective access date (reported in parentheses).