This commented course catalog provides English descriptions of selected offerings in this study program.
- Please refer to the official module handbook for a comprehensive source
- See the sample curriculum regarding ECTS volume and WS/SS parity of the offerings
P1 Stochastic Calculus and Arbitrage Theory in Continuous Time
- Content
- In the first part of the lecture, the basics of the stochastic calculus for Brownian motion in continuous time are introduced. In the second part, arbitrage theory in continuous-time market models is considered with particualr attention to the (generalized) Black-Scholes model. Further aspects are: Arbitrage-free and completeness of markets, fundamental theorems of asset valuation, arbitrage-free valuation and hedging of contingent claims, Black-Scholes formula, exotic and American options.
- Learning outcome
- The aim of the lecture is to teach the basics of the Ito calculus and arbitrage theory in continuous-time stochastic models. As a standard reference in financial markets, the Black-Scholes model is examined in detail. The module serves as a prerequisite for further courses in the field of stochastic analysis and continuous-time financial mathematics.
P2 Statistical Inference
- Content
- Based on basic knowledge from courses on statistical inference, advanced general concepts and methods of estimation and testing in statistical models are covered. After an introduciton to classical parametric estimation and test theory, the focus is on likelihood-based and Bayesian inference concepts that go beyond the simple case of i.i.d. data. Knowledge of both statistical theory and the algorithms associated with the methodology is taught. Further topics include bootstrap techniques and an introduction to non-parametric and semi-parametric methods as well as an outlook on current developments. Basic and in-depth knowledge of the most important concepts and methods of statistical inference will be acquired. Through the exemplary inclusion of statistical models and questions from different areas, an understanding of the universally applicable concepts, statistical theory and application relevance will be conveyed. The lecture develops the first central concepts and methods of estimation and test theory. Essential properties of the most important methods are formulated and their application is illustrated using examples.
- Learning outcome
- Students are expected to master the theoretical foundations and key methods of estimation and testing theory.
P3 Mathematical Seminar A
- Content
- In this seminar, students independently work on a current mathematical topic and present it in a talk to their fellow students.
- Learning outcome
- In addition to the ability to independently learn a new mathematical field, students also deepen their ability to present mathematical content to others in a clear, understandable and pedagogically meaningful way.
WP1 Financial Mathematics
- Content
- This module covers selected topics in financial or actuarial mathematics.
- Learning outcome
- The aim of the module is to convery further qualifications in financial or actuarial mathematics.
WP2 Actuarial Mathematics A
- Content
- This module covers topics in actuarial mathematics.
- Learning outcome
- The aim of the module is to convery qualifications in actuarial mathematics, including preparation for advanced actuarial training.
WP3 Elective Topics in Business Administration (Theory) I
- Content
- The course comprises advanced topics in business administration.
- Learning outcome
- The aim of the module is to expand the knowledge imparted in the basic and specialization courses to include further subject-relevant content and aspects in business administration.
WP4 Fachspezifische Grundlagen: Finance and Insurance
- Content
- The course introduces the theoretical and empirical concepts of modern finance required in advanced courses. The first part of the course seeks to deepen the understanding of why risk management is beneficial by applying classic decision theory to investment and risk management problems. The second part of the course is concerned with market risk, covering different measures of risk and return, as well as portfolio theory and common asset pricing techniques. The last part deals with credit risk, in particular the role of ratings, default correlations, credit portfolio models, such as the CreditMetrics model, as well as credit derivatives.
- Learning outcome
- The aim of the course is to convey concepts in modern finance in preparation for futher advanced courses in business admnistration.
WP5 Microeconomics
- Content
- This module comprises microeconomic topics with focus is on demand theory, general equilibrium theory, game theory, principal-agent problems and problems of adverse selection.
- Learning outcome
- Students learn to use microeconomic theories to analyze and evaluate economic issues in a well-founded manner in research and applications.
WP6 Macroeconomics
- Content
- The module comprises modern, dynamic models of macroeconomics, in particular economic growth and optimal decisions in stochastic systems as well as monetary theory under flexible and fixed prices.
- Learning outcome
- Students should be able to understand central variables of macroeconomics such as production, employment, unemployment, inflation and interest rates and develop models for macroeconomic analysis.
WP7 Econometrics
- Content
- This module comprises methods of econometrics, combining statistical estimation tools and economic theory. As part of the module, central concepts of econometrics are developed. The focus is on regression models for various data-generating processes and on suitable statistical estimation approaches.
- Learning outcome
- Students learn to use econometric methods to empirically test the predictions of theoretical models in economics and to create statistically sound forecasts of economic decisions made by individuals, households and companies. In addition, students should be able to follow the latest developments in the literature and assess their relevance for their own research projects.
P4 Numerical Methods in Financial Mathematics
- Content
- The lecture introduces some of the most important numerical methods and their implementation. The numerical methods are motivated by
applications from mathematical finance, and their functionality is
illustrated through sample implementations.
Central topics include discrete approximation schemes for stochastic
differential equations and Monte Carlo methods and their application to
stochastic differential equations. In addition, other significant methods in financial mathematics are addressed, as they are used in processing market data, model calibration, and calculating risk parameters.
The lecture also covers particular aspects of implementation, such as
floating-point arithmetic or object-oriented design. - Learning outcome
- Students learn some of the most relevant numerical methods and acquire the skill to create corresponding implementations. With the acquired knowledge, students can numerically solve problems in financial mathematics, such as the valuation of complex derivatives.
P5 Statistical Models for Financial Mathematics
- Content
- This module covers selected topics in statistical modeling with a focus on issues relevant to financial and actuarial mathematics.
- Learning outcome
- In this model, students learn the methodology and application of statistical modeling to problems in financial and actuarial mathematics.
WP8 Quantitative Risk Management
- Content
- This module deals with theoretical concepts and advanced modeling techniques of quantitative risk management in financial and insurance markets. Possible contents are: multivariate models, copulas and dependencies, risk aggregation, extreme value theory, credit risk management, operational risks, insurance risk theory, convex risk measures, financial market models with jumps (Lévyprocesses).
- Learning outcome
- The aim of this module is to introduce students to the methods and concepts of quantitative risk management. With the acquired knowledge, students are able to understand the basic structures of risk management and to apply appropriate analytical instruments in a problem-oriented manner.
WP9 Fixed Income Markets
- Content
- The lecture provides an introduction to the modeling of interest rate markets and the risk-neutral valuation of interest rate derivatives. The content includes the definition of common interest rate products (bonds, swaps, caps, floors, swaptions), yield curves and interest rate models, as well as analytical valuation approaches using the same. The interest rate models discussed include short rate models, affine term structures, Heath-Jarrow-Morton models as well as aspects of credit risk modeling.
- Learning outcome
- The aim of this module is to provide an overviw of the theory of interest rate products and interest rate modeling. With the acquired knowledge, students are able to understand in-depth relationships in of the theory and derive analytical valuation methods.
WP10 Finance and Insurance I
- Content
- The lecture introduces the theoretical and empirical concepts of modern finance required in advanced courses. The first part of the course seeks to deepen the understanding of why risk management is beneficial by applying classic decision theory to investment and risk management problems. The second part of the course is concerned with market risk, covering different measures of risk and return, as well as portfolio theory and common asset pricing techniques. The last part deals with credit risk, in particular the role of ratings, default correlations, credit portfolio models, such as the CreditMetrics model, as well as credit derivatives.
- Learning outcome
- The lecture conveys concepts in modern finance, also in preparation of further advanced courses.
WP11 Advanced Topics in Computer Science
- Content
- This module comprises selected advanced topics from the field of computer science.
- Learning outcome
- The aim of the module is to provide qualifications in the field of computer science that enable students to apply and develop computer-aided processes.
P6 Praktikum
- Content
- An internship is a professional learning experience that offers practical work related to the professions targeted by the Master's program in Financial and Actuarial Mathematics.
- Learning outcome
- The aim of the module is to offer students opportunity for career exploration and development, to learn new skills and to apply the knowledge acquired in the study programm.
WP12 Advanced Topics in Mathematics A
- Content
- This module comprises advanced areas of mathematics.
- Learning outcome
- The aim of the module is to familiarize students with advanced questions and methodological approaches in mathematics. With the acquired knowledge, they are able to work independently in the field.
WP13 Advanced Topics in Mathematics B
- Content
- This module comprises advanced areas of mathematics.
- Learning outcome
- The aim of the module is to familiarize students with advanced questions and methodological approaches in mathematics. With the acquired knowledge, they are able to work independently in the field.
WP14 Advanced Topics in Financial Mathematics A
- Content
- This module comprises advanced areas of financial and insurance mathematics.
- Learning outcome
- The aim of the module is to familiarize students with advanced questions and methodological approaches in financial and insurance mathematics. With the knowledge they have acquired, they are able to work independently in this field.
WP15 Advanced Topics in Financial Mathematics B
- Content
- This module comprises advanced areas of financial and insurance mathematics.
- Learning outcome
- The aim of the module is to familiarize students with advanced questions and methodological approaches in financial and insurance mathematics. With the knowledge they have acquired, they are able to work independently in this field.
WP16 Advanced Topics in Financial Mathematics C
- Content
- This module comprises advanced areas of financial and insurance mathematics.
- Learning outcome
- The aim of the module is to familiarize students with advanced questions and methodological approaches in financial and insurance mathematics. With the knowledge they have acquired, they are able to work independently in this field.
WP17 Mathematisches Seminar B
- Content
- In this seminar, students independently work on a current mathematical topic and present it in a talk to their fellow students.
- Learning outcome
- In addition to the ability to independently learn a new mathematical field, students also deepen their ability to present mathematical content to others in a clear, understandable and pedagogically meaningful way.
WP18 Actuarial Mathematics B
- Content
- This module covers topics in actuarial mathematics.
- Learning outcome
- The aim of the module is to convery qualifications in actuarial mathematics, including preparation for advanced actuarial training.
WP19 Actuarial Mathematics C
- Content
- This module covers topics in actuarial mathematics.
- Learning outcome
- The aim of the module is to convery qualifications in actuarial mathematics, including preparation for advanced actuarial training.
WP20 Elective Topics in Statistics and Probability
- Content
- The module covers advanced topics from mathematical statistics and probability theory.
- Learning outcome
- In the module, students acquire in-depth knowledge and methods from mathematical statistics and/or probability theory.
WP21 Statistical Methods for Financial Mathematics
- Content
- This module covers selected topics of statistical analysis with reference to problems in financial and actuarial mathematics.
- Learning outcome
- In this model, students learn the methodology of statistical analysis and its application to problems in financial and actuarial mathematics.
WP22 Advanced Topics in Computer and Data Science A
- Content
- This module covers advanced topics in the field of computer science and data science, especially but not exclusively related to automated statistical analysis and machine learning.
- Learning outcome
- The aim of the module is to provide students with qualifications in the fields of computer science and data science that enable them to apply and develop modern automated procedures for the statistical analysis of empirical data.
WP23 Advanced Topics in Computer and Data Science B
- Content
- This module covers advanced topics in the field of computer science and data science, especially but not exclusively related to automated statistical analysis and machine learning.
- Learning outcome
- The aim of the module is to provide students with qualifications in the fields of computer science and data science that enable them to apply and develop modern automated procedures for the statistical analysis of empirical data.
WP24 Elective Topics in Business Administration (Theory) II
- Content
- The course comprises advanced topics in business administration.
- Learning outcome
- The aim of the module is to expand the knowledge imparted in the basic and specialization courses to include further subject-relevant content and aspects in business administration.
WP25 Elective Topics in Business Administration (Theory) III
- Content
- The course comprises advanced topics in business administration.
- Learning outcome
- The aim of the module is to expand the knowledge imparted in the basic and specialization courses to include further subject-relevant content and aspects in business administration.
WP26 Elective Topics in Business Administration (Applied Theory) I
- Content
- The course comprises advanced topics in business administration.
- Learning outcome
- The aim of the module is to expand the knowledge imparted in the basic and specialization courses to include further subject-relevant content and aspects in business administration.
WP27 Selected Topics of Statistical Computing
- Content
- This module covers topics of computer-aided statistical analysis.
- Learning outcome
- In this module, students learn how to apply and develop automated, statistical analysis methods.
P7 Abschlussmodul
- Content
- In the final thesis, an advanced mathematical topic, possibly including current research questions, is elaborated and presented in a written form based on given references.
- Learning outcome
- Learning objectives are the training of work organization and of the ability to present a complex mathematical topic in a written form as well as the learning of techniques of scientific work in mathematics. In this way, essential key qualifications of the degree program are acquired.