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Åbo Akademi University 2014/2015
NATURAL SCIENCES
Natural Sciences
Geology
Geology is the science of the Earth´s physics, chemistry and
history. Geosciences today deal with the interaction be-
tween the lithosphere (the solid Earth), the hydrosphere, the
biosphere and the atmosphere. Geology and Mineralogy at
Åbo Akademi University educate geologists with expertise in
bedrock geology and environmental geology. Our research
is focused on
- The evolution of the Fennoscandian shield. The Fennoscan-
dian shield is the piece of Earth where we live. The old shield
contains a lot of mineralizations why the geological activity
is high in the area. For successful exploration of mineral ores,
geologists need deep knowledge in the geological history
about the area in focus. This is why the we do research on
the evolution of the Fennoscandian shield.
- Environmental mineralogy. Or "cheap solutions for global
problems". Our philosophy is that solutions of anthropogenic
environmental damages should be as energy efficient as pos-
sible. Oneway is touse "intelligent"mineralswith short carbon
track to clean the environment instead of industrial processed
chemicals with a long carbon track.
- Environmental geochemistry. Sometimes the natural envi-
ronment is polluting itself. Like the leakage of heavy metals
fromacid soils around the Baltic Sea. Our research is to identify
polluting leakages to the Baltic Sea, quantify it and create
solutions for the problem.
Petrology III - Magmatic processes
243022.0
5 credits
Advanced level
Offered: Autumn 2014
The course can be given in English if there are students
requesting it.
Course literature: Hall, Anthony: Igneous petrology (2nd edi-
tion), Addison Wesley Publishing Company
Advanced field course in petrology
243021.0
3 credits
Advanced level
Offered: Spring 2015
Form of teaching: Excursion to Brändö, Kumlinge and the
mainland of the Åland islands. Description of petrological
processes. The course can be given in English if there are
students requesting it.
Mathematics
Themain fields of research at the Department of Mathematics
of Åbo Akademi University are functional analysis with appli-
cations to complex analysis and stochastics with applications.
Many courses on the advanced level are on these and related
topics. Students attending the advanced courses are usually
supposed to have passed at least two years of mathematical
studies. All courses on the advanced level can be held in Eng-
lish, if there is a need. Courses for 1st and 2nd year students are
held in Swedishbut inmany cases the textbooks are in English.
The personnel of the department arewilling to help English-
speaking students also on the 1st and 2nd year courses but
courses on the advanced level are recommended.
Research seminars and post-graduate courses are usually
given in English.
Financial Mathematics I
273020
5 credits
Advanced level
Lectures and exercises
Offered: Autumn 2014
Lecturer/Contact: Professor Paavo Salminen
Aim: To give an introduction to the mathematical theory
for basic financial derivatives.
Contents: In the first part of the course a presentation of dif-
ferent instruments on financial markets (e.g. interest rates,
bonds, stocks, forwards, futures and options) is given. In the
second part, themathematical theory of pricing and hedging
of European options in the discrete time models is treated. In
particular, we analyze the Cox-Ross-Rubinstein binary model
in detail and derive, therefrom, the Black-Scholes formula via
a limiting procedure.
Learning outcomes: After the course the participant should
have basic knowledge of different financial instruments and
understand the mathematical theory of pricing European
options in discrete time and how the Black-Scholes formula
is derived from the Cox-Ross-Rubinstein model.
Teaching methods: Lectures and exercises (6 contact hours
per week)
Entry requirements: An intermediate course in probability
theory and real analysis.
Target group: Undergraduate (MA) and graduate students in
mathematics and statistics
Form of assessment: Homework and written examination
Course literature: The lectures are based on the following
literature:
Cox, J.C., Rubinstein, M.: Optionsmarkets, Prentice-Hall, 1985;
Foellmer H., Schied, A.: Stochastic finance; An introduction in
discrete time (2nd edition), de Gruyter 2004;
Hull, J.C.: Options, futures and other derivatives (4th edition),
Prentice Hall, 2000;
Lamberton, D., Lapeyre, B.: Introduction to stochastic calculus
applied to finance, Chapman & Hall, 1996, 2 ed. 2007;
Panjer, H.H (ed): Financial economics; with applications to
investments, insurance and pensions, The Actuarial Founda-
tion, 1998.
Financial Mathematics II
273021
5 credits
Advanced level
Lectures and exercises
Offered: Autumn 2014
Lecturer/Contact: Professor Paavo Salminen
Aim: To present the basicmathematical theory for the pricing
of European type financial derivatives in continuous time and
of American type in discrete time.
Contents: The course focusesmainly on option pricing theory.
In the first part of the course European options in the Black-
Scholes market model are considered. To understand the
mathematical framework, a short introduction to stochastic
calculus with Brownian motion is given. In the second part,
American options are analyzed in the discrete time models.
For this, some aspects of the theory of optimal stopping for
discrete time processes are presented.
Learning outcomes: After the course the participant should
understand the Black-Scholes market model and how the
