Handbook of Modules for
Master’s Programme in Actuarial and Financial Mathematics at TU Kaiserslautern
Starting:
SS 2017
This
is a translation of the German version (Master Finanz und
Versicherungsmathematik) which can be found at
http://www.mathematik.unikl.de/modulhandbuecher/
Translation errors cannot be excluded. In case of doubt only the German version
applies.
1.
Actuarial and Financial Mathematics
Probability
Concepts for Financial Markets
NonLife
Insurance Mathematics
Seminar
Actuarial and Financial Mathematics
2. Statistics
and Computational Methods
Insurance
Economics....................................................................................................... 21
Bank Management II: Bank Analysis and Management ................................................... 23
Choice under Uncertainty................................................................................................. 25
Contract Theory ............................................................................................................... 27
Dynamics of Financial Markets......................................................................................... 29
Economics of Banking...................................................................................................... 31
Investment Analysis.......................................................................................................... 33
Investment Management ................................................................................................. 35
Risk Management............................................................................................................. 37
4. Specialization Actuarial and Financial
Mathematics
Specialization
Actuarial and Financial Mathematics
Course Catalogue for Indepth modules:
ContinuousTime
Portfolio Optimization
Life,
Health, and Pension Insurance Mathematics
Markov
Switching Models and their Applications in Finance
Risk
Measures with Applications to Finance and Insurance
Reading
Course: Advanced Topics in Actuarial and Financial Mathematics
4.3 Praktikum / Projektseminar
Projektseminar
Advanced Modelling in Actuarial and Financial Mathematics
Master’s
Thesis (Masterarbeit)
NonLife Insurance Mathematics
(Schadensversicherungsmathematik)


Module
Number MAT6119M7 
Effort 270
h 
CP
(Credits) 9
CP 
Semester 1st
or 2nd 
Frequency
of occurrence every
winter semester 
Duration 1
Semester 

1 
Courses 

SelfStudy 
Intended
size of class 

NonLife Insurance Mathematics 
4 SWS / 60 lecture hours 
180 h 
2040 Students 

2 
Result
of study / competences: Students
acquire a complete overview of the modelling of loss levels, time of damage
and the reserve process under the generalized CramerLundberg model. They
understand the mathematical foundations of ruin theory and premium
calculation (in particular, the experience rating and the terms of loss
reserves and reinsurance) and are able to apply them. By
completing the exercises, students develop a skilled, precise and independent
handling of the terms, propositions and methods taught in the course. They
understand the proofs presented in the lecture and are able to reproduce and
explain them. They can in particular outline the conditions and assumptions
that are necessary for the validity of the statements. 

3 
Contents: · Convolution and Transformation · Loss Distribution · Individual risk model · Collective risk models: 
Models for the claim number process 
Poisson processes 
Renewal processes 
Total loss distribution · Risk Process · Ruin theory and ruin probabilities · Premium calculation · Experience rating: 
Bayes estimation 
Linear Bayes estimation (Bühlmann and
BühlmannStraub model · Loss reserves · Reinsurance and risk sharing 

4 
Form
of teaching: Lectures and tutorials in
small groups. 

5 
Prerequisites: Module “Probability Theory” from the Bachelor’s degree
programme in Wirtschaftsmathematik. 

6 
Type
of examination : Oral exam (individual
examination, Duration 2030 minutes). 

7 
Requirements
for the award of credits: Participation
in the end of semester examination. 

8 
Usability
of this module: This course is a compulsory
module under specialization for Master's degree in Actuarial and Financial
Mathematics. Elective module for Master’s
degree in Mathematics, Technomathematics, Economathematics and Mathematics
International. · Main focus of study is “Financial Mathematics“ or “Statistics“; · Areas of applied mathematics or general mathematics if the main focus
of study is not chosen from the list above (considering the rules of the
degree programme which might restrict the above). 

9 
Significance
towards the final grade: One receives a grade at the end of the oral examination. This comprises 9.7% of the final grade that
one receives at the end of the Master’s Program. 

10 
Reading
to complement course material: 


H. Bühlmann: Mathematical Methods in Risk
Theory, R. Kaas, M. Goovaerts, J. Dhaene, M.
Denuit: Modern Actuarial Risk Theory, T. Mikosch: NonLife Insurance: An
Introduction with the Poisson Process, E. Straub: NonLife Insurance Mathematics. 




11 
Authorised
representatives of the module : 


Prof. Dr. R. Korn, Prof.
Dr. J. Saß 




Seminar Actuarial and
Financial Mathematics


Module
Number MAT61SEMM7 
Effort 90
h 
CP
(Credits) 3 CP 
Semester 2nd or 3rd 
Frequency
of occurrence every
Semester 
Duration 1
Semester 

1 
Courses 

SelfStudy 
Intended
size of class 

Seminar <Topic of the
seminar> 
2 SWS Seminar / 30 h 
60
h 
1020
Students 

2 
Result
of study / competences: Students
learn to use scientific methods in order to work on an advanced topic in the
field of financial and actuarial mathematics autonomously. Moreover, they
present this in the form of a lecture and thus acquire expertise in the
presentation of mathematical content. 

3 
Contents: Few advanced topics from the field of
financial and actuarial mathematics will be chosen depending on the topic of
the seminar. 

4 
Form
of teaching: Seminar 

5 
Prerequisites: Depending on the choice of the topic,
different courses from the bachelor and the master degree programmes of
mathematics will be required. Formal
conditions: prior registration. 

6 
Type
of examination : Presentation and seminar
report. 

7 
Requirements
for the award of credits: ‘Seminarschein’
confirming successful participation in the seminar. The type of course work
to be done will be announced by the course conductor before the beginning of
the seminar; it would usually be a combination of an oral presentation
(duration 3090 minutes) and seminar report (seminar paper). 

8 
Usability
of this module: Elective module for Master’s
program in Actuarial and Financial Mathematics. This could also be a part of
the other Master’s degree programme under the department of mathematics. 

9 
Significance
towards the final grade: The module will not be graded. 

10 
Reading
to complement course material: 


The literature required will be announced
during the course. 




11 
Authorised
representatives of the module : 


Prof. Dr. R. Korn, Prof.
Dr. J. Saß 




12 
Additional
Information: The seminar registration and briefing usually takes place at the end
of the lecture period of the preceding semester. 

Under
the section "Statistics and Computational Methods", one has to obtain
a total of 1821 credits points from the elective modules. At least 9 CP have
to be obtained from the following modules:
Any extra
credit points required could be obtained from any of the following modules (from
other Master’s degree programme under the department
of mathematics)Modulen
aus den Masterstudiengängen des Fachbereichs Mathematik
·
„Numerics of ODE”,
·
„PDE: An Introduction”,
·
„Numerical Methods for Elliptic
and Parabolic PDE”,
·
„Extreme Value Theory“,
·
,,Statistical
Learning and Regression“,
·
„Nonlinear Optimization“,
With the approval of the examination committee, other modules in the
field of statistics and computational methods also are permitted.
Computational Finance


Module
Number MAT6114M7 
Effort 135
h 
CP
(Credits) 4,5
CP 
Semester 1st,
2nd or 3rd 
Frequency
of occurrence irregular 
Duration 1
Semester 

1 
Courses 

SelfStudy 
Intended
size of class 

Computational Finance 
2 SWS / 30 lecture hours 
105 h 
1525 Students 

2 
Result
of study / competences: Students
are able to implement the knowledge they acquired in the introductory
lectures on financial mathematics to price ratings of financial derivatives
through different numerical methods. 

3 
Contents: ·
Standard models:
BlackScholes, Heston and other SV models, local volatility ·
Choice of model and calibration ·
Options evaluation: analytical formula, PDE,
MonteCarlo simulation, trees ·
Pricing of exotic options and certificates ·
Selected topics on MonteCarlo simulations:
generation of random variables, numerical methods for SDE, variance
reduction, stochastic Taylor expansion ·
Convergence of Stochastic processes and
Donsker's Theorem. 

4 
Form
of teaching: Lectures 

5 
Prerequisites: The
course Probability Theory. Additional knowledge from ”Financial
Mathematics“ is useful but not required. . 

6 
Type
of examination : Oral exam (individual
examination, Duration 2030 minutes). 

7 
Requirements
for the award of credits: Participation
in the end of semester examination. 

8 
Usability
of this module: This course is an elective module for Master's degree in Actuarial and
Financial Mathematics. Elective module for Master’s degree in Mathematics, Technomathematics,
Economathematics and Mathematics International. · Main focus of study "Financial Mathematics“; · Areas of applied mathematics or general mathematics if the main focus
of study is not Financial Mathematics (considering the rules of the degree
programme which might restrict the above). 

9 
Significance
towards the final grade: One receives the final grade at the end of the oral examination. This comprises 4.8
% of the final grade that one receives at the end of Master’s Program. 

10 
Reading
to complement course material: 


R. Korn, E. Korn, G. Kroisandt: Monte
Carlo Methods and Models in Finance and Insurance, Ö. Ugur: An Introduction to Computational
Finance. 




11 
Authorised
representatives of the module : 


Prof. Dr. R. Korn, Prof.
Dr. K. Ritter 




The course
details for the modules mentioned here can be found in the German version here or in the Handbook of Modules
for Economics (Wirtschaftswissenschaften) here.
Insurance
Economics.
Under
elective modules in “Financial Economics“ one has to obtain 9 credit points (CP)
from the courses offered in Master’s in Economics under the title “Financial Economics“ or “Finanz
und Bankmanagement“ (link).
In particular, one could choose modules from the following list:
With the
approval of the examination board, other modules from the field of Economics
may also be permitted.
Specialization Actuarial and
Financial Mathematics


Module Number MAT6112AM7 
Effort 270 h 
CP (Credits) 9 CP 
Semester 2nd or 3rd 
Frequency of occurrence every winter semester 
Duration 1 Semester 

1 
Courses 

SelfStudy 
Intended size of class 

Interest Rate Theory Another indepth course is to be chosen from:  „ContinuousTime
Portfolio Optimization",  „Life,
Health, and Pension Insurance Mathematics”,  „Markov
Switching Models and their Applications in Finance",  „Risk
Measures with Applications to Finance and Insurance" Or another in depth
(specialization) course from the field of actuarial and financial
mathematics. 
2 SWS / 30 lecture hours 2 SWS / 30 lecture hours 
105 h 105 h 
2040 Students 1530 Students 

2 
Result of study / competences: Students understand the fundamentals of the theory of interest rate
products and modeling of interest rate markets. They are able to understand
the deep relations in the theory of interest rate modeling and analytical
evaluation process of global rates. In addition, they acquire indepth knowledge of specific concepts and
methods in other areas of financial and insurance mathematics, such as
methods for solving stochastic control problems (stochastic control, duality
approach), Markov switching models, the theory of risk measurements or
advanced topics of personal insurance. They learn to apply these methods and
are able to critically assess the implementation and application of the
theoretical results. They gain a precise and independent handling of terms, propositions
and methods of the lecture. They understand proofs presented in the lecture
and are able to reproduce and explain them. They can in particular outline
the conditions and assumptions that are necessary for the validity of the
statements and how these are to be interpreted in the context of actuarial
and financial mathematics. 

3 
Contents: Interest Rate Theory: ·
Basics of interest
modelling (Bonds and linear products, swaps, caps and floors, bond options,
rate of interest options, interest rate term structure curve, interest rates
(short rates and forward rates)) ·
Heath–Jarrow–Morton
framework (simple example: HoLee model, general HJM drift condition, one and
multidimensional modelling) ·
Short rate models
(general one factormodelling, term structure equation, affine modelling
of interest rate structure, Vasicek,
CoxIngersollRoss and further models, option pricing model, model
calibration ) ·
Defaultable bonds
(Merton model) Other specialization modules: See the corresponding
course description under Lehrveranstaltungsbeschreibung. 

4 
Form of teaching: Lectures. 

5 
Prerequisites: Module “Financial Mathematics“; Depending on the choice of the lecture,
different courses from the bachelor and the master degree programme of
mathematics will be required. Kindly refer to course description under Lehrveranstaltungsbeschreibung. 

6 
Type of examination Oral exam (individual
examination, Duration 2030 minutes). 

7 
Requirements for the award of credits: The examinations of the selected courses. 

8 
Usability of this module: This course is a
compulsory module under specialization for Master's degree in Actuarial and
Financial Mathematics. Elective module for
Master’s degree in Mathematics, Technomathematics, Economathematics and
Mathematics International. ·
Main focus of study is
“Financial Mathematics“ or “Statistics“; ·
Areas of applied
mathematics or general mathematics if the main focus of study is not chosen
from the list above (considering the rules of the degree programme which
might restrict the above). 

9 
Significance towards the final grade: One receives the final grade at the end of the oral examination. This comprises 9.6 % of the final grade that
one receives at the end of Master’s Program. 

10 
Reading to complement course material: 


Interest Rate Theory: T. Björk: Arbitrage
Theory in Continuous Time, D. Brigo, F. Mercurio:
Interest Rate Models – Theory and Practice, N. Branger, C. Schlag:
Zinsderivate – Modelle und Bewertung. Other specialization modules: See the corresponding
course description under Lehrveranstaltungsbeschreibung 




11 
Authorised representatives of the module : 


Prof. Dr. R. Korn, Prof.
Dr. J. Saß 




12 
Additional Information: Each winter semester at least one of the following courses will be
offered: „ContinuousTime
Portfolio Optimization", „Life, Health, and Pension
Insurance Mathematics”,
„Markov Switching Models and
their Applications in Finance" or „Risk Measures with
Applications to Finance and Insurance". 

As part of the specialization
modules (in depth module) a specialization course amounting to 2 hours per week
will be offered. This can be chosen from:
With the approval of the
examination committee, one is also allowed to choose other specialization
courses from the field of financial and actuarial mathematics.
ContinuousTime Portfolio
Optimization (Zeitstetige Portfoliooptimierung)


LVNumber MAT6115V7 
Effort 
LP (Credits) 
Semester 2nd or 3rd 
Frequency of occurrence irregular (in WS) 
Duration 1 Semester 

1 
Courses 

SelfStudy 
Intended size of class 

ContinuousTime
Portfolio Optimization 
2 SWS / 30 lecture hours 
105 h 
1530 Students 

2 
Result of study / competences: Students know and understand the two main methods for solving stochastic
control problems in financial and insurance mathematics, i.e. the stochastic
control approach and the duality approach. They understand the proofs
presented in the lecture and are able reconstruct and explain them. They can
use the methods on various problems of portfolio optimization and critically
assess the implementation and application of the theoretical results. They
are able to assess the applicability of a method or alternative methods under
various model extensions and restrictions to the strategies and understand
the impact these have on the optimal solutions. 

3 
Contents: ·
Introduction to
PortfolioOptimization (problem statement) ·
Continuoustime portfolio problem: expected
benefit approach ·
Martingale method for complete markets ·
Stochastic control approach (HJB equation,
verification theorems) ·
PortfolioOptimization with restrictions
(e.g. risk boundaries, transaction costs) ·
Alternative methods 

4 
Form of teaching: Lectures 

5 
Prerequisites: Module “Financial Mathematics“. 

6 
Reading to complement course material: 


I. Karatzas, S.E.
Shreve: Methods of Mathematical Finance, R. Korn: Optimal
Portfolios, R. Korn, E. Korn: Option
Pricing and Portfolio Optimization  Modern Methods of Financial Mathematics, H. Pham: Continuoustime
Stochastic Control and Optimization with Financial Applications. 




Life, Health, and Pension
Insurance Mathematics (Personenversicherungsmathematik)


LVNumber MAT6131M7 
Effort 
CP (Credits) 
Semester 2^{nd} or 3^{rd} 
Frequency of occurrence Irregular (in WS) 
Duration 1 Semester 

1 
Courses 

SelfStudy 
Intended size of class 

Life, Health, and
Pension Insurance Mathematics 
2 SWS / 30 lecture hours 
105 h 
1530 Students 

2 
Result of study / competences: Students understand the dynamic mathematical models in life insurance
and life insurance products, which allow for investment in the financial
market. In addition, they master the basic model requirements and methods of
pension and health insurance. They learn to combine techniques of financial mathematics with current
issues of actuarial mathematics and critically assess the corresponding
insurance products. Moreover, they are able to understand and apply the
concepts learnt in the module “Life Insurance Mathematics” to the specific
case of pension and health insurance mathematics. 

3 
Contents: This lecture is based
on the module “Life Insurance Mathematics”. It deals with dynamic models in
life insurance mathematics and with life insurance products which allow for
investment in the financial market. In addition, mathematical models and
specific problems of pension plans and health insurance are addressed. The
following topics are covered: Life Insurance Mathematics: ·
Dynamic models (Markov
chain, continuous time), ·
Stochastic interest
rates, ·
Products with investment
in the financial market and guarantee funds, ·
Market consistent
valuation. Actuarial Mathematics for Pension Plans: ·
State diagrams and
benefits, ·
Neuburger's model, ·
Estimation of decrement
rates, ·
Premiums and actuarial
reserves. Health Insurance
Mathematics: ·
Premium principles, ·
Reserves for increasing
age and contract changes, ·
Profit participation and
premium reductions , ·
Risk assessment. 

4 
Form of teaching: Lectures. 

5 
Prerequisites: Module “Financial Mathematics“ and “Life Insurance Mathematics“. 

6 
Reading to complement course material: 


M. Koller: Stochastic
Models in Life Insurance, H. Milbrodt, M. Helbig:
Mathematische Methoden der Personenversicherung. 




Markov Switching Models and
their Applications in Finance


LVNumber MAT6120V7 
Effort 
LP (Credits) 
Semester 2nd or 3rd 
Frequency of occurrence Irregular (in WS) 
Duration 1 Semester 

1 
Courses 

SelfStudy 
Intended size of class 

Markov Switching Models
and their Applications in Finance 
2 SWS / 30 lecture hours 
105 h 
1530 Students 

2 
Result of study / competences: Students know and understand properties of Markov switching models
that are suitable for modeling financial time series and their application,
both in discrete and continuous time. They can critically analyse different
modeling approaches. They also understand the theoretical foundations of
filter theory, the methods for parameter estimation and model selection and
know how these can be implemented. With regard to the predictability of
application and its comparison with econometric properties of financial time
series, they are able to make a reasonable choice of models for various
applications in financial mathematics and time series analysis. They
understand the proofs presented in the lecture and are able to reproduce and
explain them. 

3 
Contents: ·
Discretetime and
continuoustime Markov chains, ·
Hidden Markov models in discrete time, ·
Continuous time Markov switching models ·
Parameter estimation and filtering ·
Modeling financial asset prices ·
Econometric properties of financial time
series and model extensions, ·
Applications to portfolio optimization 

4 
Form of teaching: Lectures 

5 
Prerequisites: Module “Mathematical Statistics" or “Probability Theory". Knowledge of
modules “Time Series Analysis “ or “Financial Mathematics“would be useful, but not necessarily
required. 

6 
Reading to complement course material: 


A. Bain, D. Crisan:
Fundamentals of Stochastic Filtering, O. Cappé, E. Moulines,
T. Rydén: Inferences in Hidden Mrkov Models, R.J. Elliott, L. Aggoun,
J.B. Moore: Hidden Markov Models – Estimation and Control, S. FrühwirthSchnatter:
Finite Mixture and Markov Switching Models, J.R. Norris: Markov
Chains, R.S. Tsay: Analysis of
Financial Time Series. 




Risk Measures with Applications to Finance and Insurance


LVNumber MAT6130M7 
Effort 
LP (Credits) 
Semester 2nd or 3rd 
Frequency of occurrence Irregular (in WS) 
Duration 1 Semester 

1 
Courses 

SelfStudy 
Intended size of class 

Risk Measures with
Applications to Finance and Insurance 
2 SWS / 30 lecture hours 
105 h 
1530 Students 

2 
Result of study / competences: Students know and understand the basics of axiomatic theory of risk
measures. They can classify different risk measures and assess the advantages
and disadvantages of specific risk measures in various fields of finance and
insurance mathematics. They understand the proofs and are able to reproduce
and explain them. They can critically assess the different rating procedures
and methods for the measurement of credit risk. 

3 
Contents: ·
Preferences and expected
utility, ·
Axiomatic introduction
of risk measures, ·
Robust representation of convex and coherent
risk measures, ·
Examples: Value at Risk, Average Value at
Risk, Short case, worst case, ·
Extensions: Semi Dynamic, dynamic,
distributionfree risk measures, ·
Estimation of risk measures, ·
Rating systems: 
Scorebased ratings, 
Utility based ratings of financial products, 
Riskclasses for insurance products,, ·
Credit risk: Structural
models and reduced form models, ·
Applications: 
Riskbased insurance
premiums, 
Portfolio optimization
under risk constraints, 
Credit derivatives. 

4 
Form of teaching: Lectures 

5 
Prerequisites: Module “Financial Mathematics“. 

6 
Reading to complement course material: 


H. Föllmer, A. Schied:
Stochastic Finance: An Introduction in Discrete Time, L. Rüschendorf:
Mathematical Risk Analysis. 




The department of mathematics offers various courses
for guided independent academic work (“Reading Courses”), the topics for which
change every semester and are often based on current research topics.
Towards the
end of the lecture period each semester, the courses offered in various fields
under “Reading Course” are presented by the working groups through an
informative meeting.
In the master’s
program "Financial and Actuarial Mathematics", one has to complete
such a course amounting to 6CP.
Reading Course: Advanced Topics in
Actuarial and Financial Mathematics


Module Number MAT61RCM7 
Effort 180 h 
CP (Credits) 6 CP 
Semester 2^{nd} or 3^{rd} 
Frequency of occurrence Every semester 
Duration 1 Semester 

1 
Courses 

SelfStudy 
Intended size of class 

Reading Course <topic> 
n.V. 
n.V. 
3 – 15 Students 

2 
Result of study / competences: Using prescribed texts, students learn to work on an advanced topic in
the field of financial and actuarial mathematics independently. They are
prepared to work on their Master thesis in the chosen area of specialization. 

3 
Contents: The topics are usually
chosen from current areas of research (e.g. "applications of BSDE in
Financial and Actuarial Mathematics"), research topics with practical
relevance (e.g. "The mathematics behind Solvency II") or classical
areas that could not be covered in a lecture (e.g. reading research papers
from the early stages of Financial Mathematics). 

4 
Form of teaching: Reading Course 

5 
Prerequisites: Depending on the choice of the topic, different courses from the
bachelor and the master degree programmes of mathematics will be required. Formal conditions: prior registration. 

6 
Type of examination : Presentation, scientific
discussion and/or report submission. 

7 
Requirements for the award of credits: “Schein” certifying successful participation in the reading course. 

8 
Usability of this module: Elective module for
Master’s program in Actuarial and Financial Mathematics. (Specialization). Elective module for Master’s degree in Mathematics,
Technomathematics, Economathematics and Mathematics International. This can be considered as a module under specialization when the main
focus of study is Financial Mathematics. This module provides a
basis for master's thesis and other research in the field of financial
mathematics. 

9 
Significance towards the final grade: The module will not be graded. 

10 
Reading to complement course material: 


Depends on the topic. 




11 
Authorised representatives of the module : 


Prof. Dr. R. Korn, Prof.
Dr. J. Saß 




Projektseminar Advanced Modelling in
Actuarial and Financial Mathematics


Module Number MAT61PROJM7 
Effort 180 h 
CP (Credits) 6 CP 
Semester 3^{rd} 
Frequency of occurrence Every semester 
Duration 1 Semester 

1 
Courses 

SelfStudy 
Intended size of class 

Projektseminar Advanced
Modelling in Actuarial and Financial Mathematics 
2 SWS / 30 h 
150 h 
3 – 15 Students 

2 
Result of study / competences: Students are able to apply the acquired knowledge to practical
problems of financial and actuarial industry. They can gather the knowledge
required, develop and implement their solutions independently. Through the
presentation, they display their understanding of the problem and the methods
used to analyse the same. 

3 
Contents: Working on a project
from the field of finance and insurance sectors in a group (25 participants)
under the guidance of a project supervisor: ·
Starting point is
a real life problem. ·
Handling the problem:
Problem solving: selection or development of an appropriate financial or
actuarial model, gathering the required theoretical knowledge, formulating
solutions, development of theoretical solutions or selection of suitable
numerical methods, implementation of the method. During the regular meetings
with the supervisor, a group member should present the current state of work
and plan for further action. ·
Final presentation and
/ or final report: Each member of the group would be
responsible for a certain part of the project. 

4 
Form of teaching: Project based seminar. 

5 
Prerequisites: Depending on the choice of the topic, different courses from the
bachelor and the master degree programmes of mathematics will be required. Formal conditions: prior registration, eligibility to participate
might depend on whether the student has passed certain specific modules from
“Actuarial and Financial Mathematics”.
Participation criterion might also depend on the number of credit points
the student has accumulated. 

6 
Type of examination : Presentation and/or
report submission. 

7 
Requirements for the award of credits: “Praktikumsschein” certifying successful participation in the project
based seminar. With the approval of the
examination board of the department of mathematics, this module can be
replaced by an external (jobrelated) internship, provided it is ensured that
the abovementioned results of study / competences are achieved. The
presentation or report submitted should be edited to ensure that
enterprisespecific features are taken into account. 

8 
Usability of this module: Elective module for
Master’s program in Actuarial and Financial Mathematics. (Specialization). 

9 
Significance towards the final grade: This module will not be graded. 

10 
Reading to complement course material: 


 




11 
Authorised representatives of the module : 


Prof. Dr. R. Korn, Prof.
Dr. J. Saß 




12 
Additional Information: Registration and briefing for the project seminar usually takes place
at the end of the lecture period of the preceding semester. 

Master’s Thesis


Module Number  
Effort 900 h 
CP (Credits) 30 CP 
Semester 4 
Frequency of occurrence every semester 
Duration 6 Months 

1 
Courses: 

SelfStudy 
Intended size of class 

none 
 
900 h 
One person, in exceptional cases, small groups (considering the rules
of the degree programme and examination regulations). 

2 
Result of study / competences: Students are able to: · Work on a mathematical problem
autonomously within a given period of time. Hence use and apply the
scientific methods and the technical and methodological competences acquired
during their study, · Critically interpret scientific
results and integrate them into the respective knowledge. · Present their results in writing
according to the principles of good scientific practice. 

3 
Contents: Advanced
mathematical problem in the field of Actuarial and Financial Mathematics. 

4 
Form of teaching: Thesis: under the guidance of a supervisor, the students have learned
to work on an advanced mathematical topic on the basis of given literature,
using scientific methods. They are able to write a scientific master’s thesis
in their chosen main focus of study. 

5 
Prerequisites: Recommended: Modules offered under "Actuarial and Financial Mathematics"
(incl. Specialization), seminars and Reading Courses; depending on the
thesis, knowledge from other modules of the master’s program. Formal: One should have completed a minimum of 60 CP to start working on the
master’s thesis. 

6 
Type of examination : Final report has to be submitted, which would be graded. 

7 
Requirements for the award of credits: Timely submission of the thesis report, final grade
of 4.0 or better awarded by the examiners. 

8 
Usability of this module: Compulsory module for
Master’s program in Actuarial and Financial Mathematics. 

9 
Significance towards the final grade: The grade that one receives for the thesis report comprises 31.9% of the final grade that one receives at the end of
Master’s Program. 

10 
Reading to complement course material:



Ask the supervisor, also
refer to 12 (Additional Information). 




11 
Authorised representatives of the module : Faculty members of the department of mathematics. 

12 
Additional Information: Information about the thesis is
given in specific information sessions at the end of each lecture period.
Students should contact the lecturers of the chosen specialization in time,
at the latest at the beginning of the second year of their study, to collect
information about the range of topics and the necessary contentrelated
requirements.

