Teaching

Statistics I

Content of this lecture are the basics of descriptive statistics and the introduction to statistical methods. In the first part of the lecture series Statistics (consisting of Statistics I and II) the following four topics will be examined:

1. Statistical variables and their distributions
2. Characteristic measures of statistical distributions
3. Two-dimensional distributions, conditional distributions and statistical dependencies
4. Introduction to regression analysis

Literature

1. Schira: Statistische Methoden der VWL und BWL. current edition. Pearson, Hallbergmoos
2. Bleymüller, Gehler and Gülicher: Statistik für Wirtschaftswissenschaftler. current edition. Verlag Franz Vahlen, Munich

Statistics II

Based on the first part of the lecture series Statistics, Statistics II teaches the basics of probability theory and stochastics as well as an introduction to statistical estimating and statistical hypothesis testing. The following six topics are covered in the lecture:

1. Fundamentals of probability theory, conditional probability and stochastic independence
2. Stochastic variables and their distributions
3. Characteristic measures of probability distributions and multidimensional random variables
4. Stochastic models and certain distributions
5. Statistical estimators
6. Hypothesis testing

Literature

1. Schira: Statistische Methoden der VWL und BWL. current edition. Pearson, Hallbergmoos
2. Bleymüller, Gehler and Gülicher: Statistik für Wirtschaftswissenschaftler. current edition. Verlag Franz Vahlen, Munich

Project Studies

Following an introduction to good scientific practice and working, the students will deal with a selected method of multivariate data analysis (e.g. logit model, CART) in the first part of the course and learn how to use suitable statistical software. In the second part, the students work in groups to analyse a real data set under given questions and derive recommendations for actionS based on the data. The results are presented by the group and described in detail in a project report.

Econometrics

A reliable forecast of future economic developments is becoming increasingly important. Based on fundamental statistical knowledge, the lecture develops models which, under certain assumptions, are best possible for a forecast in the well-defined sense. It then discusses how to verify the assumptions made and how to modify the methods if necessary.

Literature

1. von Auer: Ökonometrie: Eine Einführung. current edition. Springer Gabler, Berlin et al.

Decision Theory

In this lecture general principles for decision making in different scenarios will be examined.  If the result of a decision option is determined, certainty is given; if, on the other hand, it is subject to stochastic influences, we speak of uncertainty. If it is possible to describe these stochastic influences exactly, then these are decision processes under risk. For example, a stochastic influence would be given by the probabilities of occurrences of possible scenario conditions at the end of a one- or multi-period planning horizon. Due to their importance for risk management, decision-making processes under risk are a central theme of this lecture. Of particular importance in this context is also determining the parameters necessary for defining the stochastic model and whether the associated costs are related to the benefits.

Literature

1. Laux: Entscheidungstheorie. current edition. Springer Gabler, Berlin
2. Bamberg, Coenenberg: Betriebswirtschaftliche Entscheidungslehre. current edition. Vahlen, Munich

Risk Management

Two Nobel Prize-winning areas of risk management are portfolio optimisation and option pricing theory. During the lecture both areas will be studied in detail. In addition to dealing with the necessary formalisms, this includes – in particular – an examination of the practicability of these theories in daily practice on the capital markets, using econometric methods.

Literature

1. Albrecht and Maurer: Investment- und Risikomanagement. current edition. Schäffer-Poeschel, Stuttgart
2. Hull: Optionen, Futures und andere Derivate. current edition. Pearson, Hallbergmoos

Insurance Statistics

The aim of every insurance is to spread the risks over a collective (which should be as homogeneous as possible). From the policyholder's point of view, the applied premium for inclusion in the collective may neither be too high nor too low. On the one hand, the economic benefit of the individual is diminished with increasing premiums and, on the other hand, the probability of ruin of the collective increases with decreasing premiums when losses due to case claims occur. The lecture will first address the question of how an insurer can put together suitable collectives. Subsequently, different models in the context of premiums and ruin probabilities will be discussed.

Literature

1. Schmidt: Versicherungsmathematik. current edition. Springer, Berlin et al.

Master Seminar

The aim of the master seminar is to deepen the theoretical knowledge already acquired in the field of statistics through scientific work. The topics of the seminar are tailored to the current research focus of the chair, but are always within the area of statistical analysis and multivariate data analysis.