Course Descriptions A  F
Course Descriptions

Advanced Financial Intermediation
Why are financial intermediaries such as banks and mutual funds different from other industries? How did Lehman Brothers' bankruptcy bring financial systems worldwide to the brink of collapse? What is the "shadow banking system" and how on earth are individual hedge fund managers able to earn more than one billion dollars per year? Contents: Principles of financial intermediation, commercial banks, other lending institutions, insurance companies, securities firms and investment banks, mutual funds, pension funds, hedge funds, private equity and venture capital, rating agencies, shadow banking system, the financial crisis, the European sovereign debt crisis, regulation of financial intermediaries.

Advanced Topics in Insurance and Finance
The course covers optimal stopping time and American options, stochastic interest rates and mortality models, and optimal asset allocation in life/pension insurance.

Analysis of Longitudinal Data
Longitudinal data arise when the same individual/experiment unit is measured at a sequence of observation times. Such data combine aspects of both multivariate data and time series. Specific to longitudinal data is that the temporal interdependence implies a highly structured pattern and that typical data sets consist of a moderate to large number of short series, one from each subject.

An Introduction to Measuretheoretic Probability
This course covers the basic facts from probability in a measuretheoretic approach. Specific topics are the definition and properties of measure and Lebesgue integral, fundamentals of probability (probability space, random variables, conditional expectation, modes of convergence, convolutions and characteristic functions, central limit theorem) and an introduction to fundamentals of statistics (simple random sampling, introduction to estimation techniques).

Asset Liability Management
AssetLiabilityManagement (ALM) describes the management and controlling of liabilities and assets within an insurance company. It is based on techniques from actuarial science and financial mathematics. The course covers the most important methods, which are widely used in practice. These methods become more and more relevant for the riskmanagement and controlling of insurance companies (e.g. due to the "Solvency II" requirements). The course discusses models, which handle the entire insurance company, as well as models, which focus on single insurance products and the matching of insurance guarantees and the asset allocation.

Asset Pricing
Go to the heart of things. Why is gold attractive even though its average return is low? Read papers which earned their authors the Nobel Prize. Learn why psychology matters for finance. Contents: Review of standard asset pricing models, equity premium puzzle, crosssection of returns, behavioral finance.

Asymptotic Statistics
This course covers selected topics from the asymptotic theory of estimators and tests. It deals with density estimators, the construction of confidence intervals and the development of asymptotic test approaches. Special attention is given to distributionfree resampling tests, like rank tests, and their application for testing non or semiparametric hypotheses.

Asymptotic Statistics A
Many of the classical statistical inference procedures need specific and stringent distributional assumptions which are often not met in practice. In the course it is shown how the tools of asymptotic statistics may provide a way out. In particular, the construction of asymptotic estimates, confidence intervals and tests is studied covering topics such as asymptotic (relative) efficiency, likelihoodratio statistics, nonparametric density estimation, rank tests, resampling (e.g. bootstrapping and permutating), U and Vstatistics.

Behavioral Economics
Behavioral economics extends the narrow view of standard microeconomics that agents are completely rational and selfish. Students will first learn to identify behavior and judgement that systematically deviates from the predictions of standard microeconomics. We will try to explain such behavior by building on concepts from neighboring disciplines, like psychology or sociology. Finally, we will focus on how behavioral theory is built upon the empirical and experimental evidence to arrive at descriptively more accurate models of human behavior. Contents: Behavioral decision theory, time inconsistency and selfcontrol, behavioral game theory, social preferences and fairness, applications to financial markets.

Behavioral Finance
Behavioral Finance explains financial phenomena by agents who are bounded rational. It consists of two building blocks: the limits to arbitrage and investor psychology. The aim of this lecture is to give students an overview over the field of behavioral finance. At the end of the semester students should know under which conditions arbitrage does not work, how behavioral patterns guide agents' investment decisions, when herd behavior occurs and what implications bounded rationality has for market outcomes.

Big Data Analytics  Methoden und Anwendungen
Through e.g. social media or the internet (online social networks, wikis, evaluation or review communities and panels) nowadays firms have access to ever growing amounts of data. Analysing this data enables improved decision making and shows great potential for different applications such as innovation management, product development, marketing, customer relationship management and many more.
Students get to know the basic theoretical background and methodologies needed in order to understand potentials and risks associated with Big Data Analytics and to successfully deal with large amounts of structured or unstructured data. 
Business Unit Strategy and Corporate Finance
The course deals with the interrelation of strategic considerations and corporate finance. For instance, we will also compare the pros and cons of different forms of capital (bank loans, bonds, equity, convertibles etc.) to fund growth. We will also discuss the different financial exit strategies (spin off, auction, leveraged buyout etc.) if a company decides to splitoff a segment that is considered noncore by its management. Contents: Recap finance basics, growth strategies, corporate restructuring, distribution mechanisms, capital structure, rating management, agency issues, incentive systems, real option valuation, risk management and hedging.

Corporate Controlling
The lecture discusses controlling in the context of management and corporate governance, and topics and dimensions of management control as well as challenges and critical success factors. Selected case studies focus on topics as the Balanced Scorecard, ITsupported controlling, processoriented controlling, profitability of investments and specific indicator systems.

Corporate Governance and Finance
When the suppliers of finance (shareholders) are distinct from those who control and operate their assets (managers)  the necessity of corporate governance comes into play. Corporate governance tries to resolve the inherent problems related to the separation of ownership and control in corporations and to alleviate the consequent agency problems  when managers want to act for their own benefit and expropriate the shareholders.

Corporate Strategy
The course covers corporate strategy fundamentals and terminology as well as strategic aspects of corporate governance, organization, and leadership, marketing, branding, and sales, supply chain management, megatrends, corporate social responsibility, innovation management, organic and acquired growth, controlling and risk and management under uncertainty.
Example contents are the definition of strategy as a core corporate process, growth/share matrix and its implications, market activated corporate strategy framework and capital market based strategies.

Credit Analysis
Acquire the risk management tools that you need to know in banking as well as in industrial firms and consulting: Make you familiar with stateofthe art credit analysis used by banks, rating agencies, fund management and supervisory authorities. Topics of the lecture include rating methods, validation of rating systems, portfolio credit risk models and bank regulation.

Data Analysis: Description, Inference and Causality
Typically the student of econometrics is presented with a bewildering range of statistical tools and methods, which differ in the assumptions that are made, in their properties and in what we learn with them from data. The reasoning of choices made, often remains unexplained (why does OLS focus on the conditional mean and not on the median or the whole conditional distribution) or is related in a rule of thumb fashion to the type of data (fixed or random effects estimators for panel data). But often real world data do not neatly fall in one of the categories and even if they do, many approaches remain to choose from. In this course we review a broad range of approaches and try to shed some light on how applied researchers choose specifications and estimation methods. We do this by considering the following three categories: Description, inference and causality.

Extreme Value Theory
Extreme Value Theory is a part of stochastics which deals with maxima and minima of random variables, records and extremely rare events. Maxima and minima of random variables play an important role in many areas, for example in sports records, extreme meteorological events or extreme events in insurance mathematics. The lecture covers topics such as limit distributions of the maximum, statistical applications, records and limiting distributions of further quantiles.

Financial Mathematics I
This course covers the fundamental principles and techniques of financial mathematics in discrete and continuoustime models. Specific topics are financial market models in discrete time (arbitrage freeness and completeness), valuation of European, American and pathdependent options, foundations of continuous time market models and of the BlackScholes model, interest rate models and derivatives, risk measures, portfolio optimization and CAPM.

Financial Mathematics II
Topics discussed in this course include stochastic analysis (stochastic integration, stochastic differential equations, (semi)martingales), continuoustime financial market models, valuation and hedging of derivatives in complete and incomplete financial markets, stochastic volatility and interest rate models (term structure modeling, interest rate derivatives, LIBOR market models).

Financial Modeling
Implement financial methods on the PC with Excel. Learn to do things in 2 minutes for which others need 2 days. The course covers topcis such as present value calculations, bond pricing, working with data and financial models, trading strategies and risk and return.

Financial Statement Analysis
The course includes topics such as ratios of financial statement analysis, investment analysis, financing analysis, liquidity analysis, Economic Value Added, Cash Value Added, Cash Flow Return on Investment, intercompany profit and loss, and ad hoc disclosure.
Course Descriptions G  O
Course Descriptions

Graph Theory I
Whenever data is arranged in a network, graphs are the language of choice to represent the data. Examples are the street layout in a city that may be used in routing problems, or relationships in a social network, or dependencies in a software project. In this course we study the theoretical properties of graphs. Apart from the many applications of graphs, they turn out to be a source of attractive results and open problems.

Graph Theory II
Graph theory offers a rich choice of attractive theorems, methods and open problems. While normally we introduce a wide range of topics in Graph Theory I, we see Graph Theory II as an opportunity to concentrate on fewer topics but deeper and more powerful techniques. Topics that we likely treat are list colouring, combinatorial Nullstellensatz, nowherezero flows, dual graphs, extremal graphs and the regularity lemma.

High Performance Computing I
This lecture provides an introduction to parallel computer architectures and standard programming interfaces for parallel numerical algorithms. We focus on few numerical algorithms like dense matrix multiplications and LU decompositions which allow us to approach step by step the theoretical peak performance.
Topics of the lecture are an introduction to the programming language C++ with a special focus on numerical linear algebra, memory hierarchies, and parallel computer architectures such as shared memory with POSIX threads and OpenMP, distributed systems with MPI and GPUs.

High Performance Computing II
Contents of this lecture are the architecture of parallel computers, parallelization, MPI, Cuda, the cluster Pacioli, Parallel Finite Elemente Method, parallel numerical methods for linear systems of equations, domain decomposition, parallel preconditioning, parallel multigrid methods, symmetric Eigenvalue problems and storage formats for sparse matrices.

Informationsverarbeitung für Aktuare
The course deals with the following topics: The meaning of information processing for actuaries, processes and applications, management of products and contracts, digitalisation and new business models, data quality, financial reporting and solvency II, quality management.

Insurance Economics
This course provides an introduction to insurance economics, including topics such as choice under uncertainty (expected utility theory and rational decision under risk, measure for risk aversion, mean variance preferences), insurance demands by households (base model, insurance demand without fair premium, Paretooptimal insurance contract), insurance demand by firms (risk management and diversification, risk management forward, future and options, corporate demand for insurance), insurance supply (traditional premium calculation, financial modelling of insurance pricing, economies of scope, economies of scale), microeconomic analysis (moral hazard, adverse selection) and insurance regulation.

Interest Rate Models
Interest rates are of fundamental importance in the economy in general and in financial markets in particular. Empirical observations suggest that they should be modelled by a stochastic process, since they are heavily varying over time. Even when considering only "risk free" interest rates there is not only a single interest rate to be modelled, but a whole interest rate curve/term structure of interest rates.
In this course we first look at the different possible interest rates and some related financial contracts and discuss ways of estimating the whole term structure based on the interest rates actually observable. Thereafter we turn to the analysis of some models for interest rates, viz. short rate models, LIBOR market models and the HeathJarrowMorton Methodology. Furthermore, forward measures, forward and futures contracts and consistent term structure parametrizations are to be considered. Furthermore we look at affine processes and how to incorporate default risk. 
Introduction to Survival Analysis
Timetoevent data are ubiquitous in fields such as medicine, biology, demography, sociology, economics and reliability theory. In biomedical research, the analysis of timetodeath (hence the name survival analysis) or time to some composite endpoint such as progressionfree survival is the most prominent advanced statistical technique. One distinguishing feature is that the data are typically incompletely observed  one has to wait for an event to happen. If the event has not happened by the end of the observation period, the observation is said to be rightcensored. This is one reason why the analysis of timetoevent data is based on hazards. This course will emphasize the modern process point of view towards survival data without diving too far into the technicalities.

Investment and Risk Management
This course deals with topics such as the classic Markowitz analysis, trackingerror minimization, indices and index tracking, portfolio insurance, risk measurement beyond singleperiod meanvariance (shortfall risk, Value at Risk) and investment styles.

Issues in Emerging Market Finance
Emerging markets are becoming an increasingly significant part of the global economy and financial markets. By almost any measure, the strength and growth of emerging market economies is impressive. Clearly, many investors recognize the potentially attractive return characteristics and diversification benefits of this asset class. Yet, institutional investors have been cautious in their allocations to emerging market equities and emerging market equities still comprise a relatively small percentage of global market capitalization and institutional investor portfolios. Emerging markets, therefore, present an enigma.
In this course we will visit some of the issues associated with emerging markets characteristics, espescialy growth drivers in emerging markets, understanding the four majors BRIC, other emerging markets, understanding financial crisis in emerging markets, formal versus informal finance in emerging markets, understanding micro finance institutions and issues in risk management.

Joint Models
A classical example from medical research is timetodeath in HIV patients and CD4 cell counts; the latter measure viral load. However, the distinction between the analysis of survival data and the analysis of longitudinal measurements is artificial. Joint models aim at an integrated analysis. As these models may not have found their final form yet, the lecture potentially touches upon rather recent research work towards the end of the semester, including causal modeling and updated prediction.

Levy Processes
Topics discussed in this course include infinitely divisible distributions, the LévyKhintchine formula, existence of Lévy processes, moments of Lévy processes, stable distributions and stable Lévy processes, and the LévyItôdecomposition and applications.

Life, Health and PensionsMathematics
This introductory course deals with the mathematical fundamentals of life, health and pension insurance. It covers basic probabilistic models for the computation of future lifetimes and lifetables, actuarial present values, expected payoffs and safety margins. With a focus on the German market, the course discusses: the calculation of premiums (principle of equivalence) for immediate and deferred life annuities, pure endowment, life insurance, health insurance and corporate pension schemes; the calculation of actuarial reserves; and the distribution of surpluses.

Management of (Re)Insurance Companies
This is a special course in reinsurance in cooperation with SCOR Reinsurance. The course will discuss links between reinsurance and financial modeling. During the course the students will work in groups on a set of problems and present their solutions.

Mathematics of Games
Game theory is the study of multiperson decision problems. Such problems arise frequently in competitive scenarios where knowledge is distributed, such as in economics. For instance, oligopolies incorporate multiperson problems: Each one must consider what the others will do in order to achieve success in a competitive environment. The same happens in auctions, where several people might be interested in the very same item. How to act in the best of ways when competition is present among participants with conflictive interests? Does cooperation help in such a scenario? In which cases?
In this class, we will cover a handful of models in game theory, including models of static and dynamic information, as well as of complete and incomplete information. We will also study a variety of stable optimal solutions, including: nash equilibrium, subgameperfect equilibrium, bayesian equilibrium, perfect bayesian equilibrium. Several examples are given, such as in the context of oligopolies, auctions, bargaining, tariff and wage competition, cooperative games, finite and infinite repeated games, zero sum games, signaling games, mechanism design, reputation.

Methods of Monte Carlo Simulation
This course gives a broad overview of Monte Carlo methods. These methods include many important tools for students interested in applied probability, finance and statistics. The course will cover the following topics pseudorandom numbers and quasirandom numbers, generating random variables, mathematical analysis of Monte Carlo algorithms and variance reduction. Examples will be given of applications in finance, probability, statistics and the physical sciences.

Numerical Finance
Prices of options cannot be computed by evaluating a simple formula if the market model is only slightly more complex than BlackScholes or if option structures are more complex. How can you price options in such cases and how can you guarantee accuracy of the computations? Contents: Generation of random numbers, MonteCarlo and QuasiMonteCarlo methods, numerical methods for the computation of European and American options: binomial, finite difference and finite element methods, numerical methods for the simulation of stochastic processes: numerical treatment of stochastic differential equations.

Operationelles Risiko – Einführung in die Theorie und Praxis bei Versicherungen
The course gives pracital introduction to currently used statistcal models for operational risk. Topics of the course include internal and external operational risk data, parametric and semiparametric models for severities, combining operational risk data sources, underreporting and scenario analysis.

Optimization and OR 2
After concentrating on linear programming, integer linear programming, and some efficiently solvable discrete optimization problems in Optimization and OR 1, in Optimization and OR 2 we will focus on algorithmically hard problems, complexity theory, approximation algorithms, and heuristics. Furthermore, we will extend some of the fundamental results of linear programming to more general, and, in particular, convex optimization problems.

Organizational Economics
Incentive problems arise in any organization. How can employers design compensation schemes or jobs to induce workers to act in their interest? Contents: Theoretical models of team work and tournaments and their predictions of individual behavior, empirical and experimental evidence on actual behavior, implications of nonstandard preferences.
Course Descriptions P  Z
Course Descriptions

Practical Actuarial Science
The Practical Actuarial Science course covers in particular the features of innovative life insurance products, simulation with MS Excel and VBA and taxation.

Practical Financial Engineering
This course offers an introduction to the practical application of tools for pricing and hedging of standard or complex derivative instruments, advanced stochastic simulation and numerical routines.

Random Fields
This is an introductory course in the theory of random functions and fields. It provides an extension of some topics treated in the course "Stochastic II", by studying random processes with a spatial index.The main topics are Kolmogorov's existence theorem, stationarity and isotropy, basic models of random fields, correlation theory of stationary random fields, positive semidefinite functions, orthogonally scattered measures and stochastic integration.

Research in Finance
This course is designed to prepare students for doing their own research projects in Finance. Students will learn how use Stata and how to manage data, how to visualize and clean data, and how to run and interpret cross sectional and panel regressions. Students are required to solve several empirical problems on their own.

Risk Management Roundup
This course gives a brief introduction to finance and business ethics. Moreover, students will study the Financial Risk Manager Handbook and prepare presentations on key concepts used for the management of different types of risk such as market risk, liquidity risk, credit risk and operational risk.

Risk Theory I: Statistical Methods of Risk Theory
This course provides an introduction to several stochastical and statistical methods of risk modeling and their applications. Some of the subjects discussed in the lecture are risk measurement using VaR and TVaR, relevant distribution families in risk theory, the collective model, credibility theory, statistical methods in risk theory, generalized linear models and their applications in risk theory, Monte Carlo simulations, mortality modeling, and stochastic processes in risk theory with focus on Markov chains and Markov processes.

Risk Theory II
This course provides an introduction to the mathematical models of (nonlife) insurance with emphasis on premium calculation, reinsurance, ruin probabilities, claim reserving, Biometric Actuarial Bases, credibility theory, simulation and MarkovChains.

Stable Distributions
In modern applications, there is a need to model phenomena that can be measured by very high numerical values which occur rarely. In probability theory, one talks about distributions with heavy tails. One class of such distributions are stable laws which (apart from the Gaussian one) do not have a finite variance. They possess a number of striking properties which make them inevitable in modelling of processes in radioelectronics, engineering, radiophysics, astrophysics and cosmology, finance, insurance, etc., to name just a few. This introductory lecture is devoted to basic properties of such distributions.
Main topics are stability with respect to convolution, characteristic functions and densities, NonGaussian limit theorem for i.i.d. random summands, representations and tail properties, symmetry and skewness and simulation. Further topics are multivariate stable distributions and elementary stable random processes.

Stochastic geometry II
Stochastic geometry deals with random geometric structures. Stochastic geometry II covers two selected topics from stochastic geometry: Random compact sets and random tesselations. More precisely, the course investigates the stochastic properties of the convex hull of random points and the most important models for random tesselations as well as the corresponding geometric quantities of the soformed cells.

Stochastics II
The course Stochastics II gives an introduction to different classes of stochastic processes. Key aspects are counting processes and renewal processes, Poisson point processes, the Wiener process, martingales, Lévy processes and stationary processes in discrete time. We shall discuss analytic, geometric and asymptotic properties of stochastic models to provide the students with knowledge of statistical methods and simulation algorithms.

Stochastics III
The lecture "Stochastics 3" is a fundamental part of each statistical education, in which especially estimation and testing in linear models is covered. These models are among the most important models in Statistics and the corresponding procedures are widely used in modeling and evaluation of various statistical problems. Topics covered include multivariate normal distribution, random quadratic forms, LeastSquares and BLUEestimators, Analysis of Variance (ANOVA) and regression analysis.

Survival and Event History Analysis
Timetoevent data are omnipresent in fields such as medicine, biology, demography, sociology, economics and reliability theory. In biomedical research, the analysis of timetodeath (hence the name survival analysis) or time to some composite endpoint such as progressionfree survival is the most prominent advanced statistical technique. At the heart of the statistical methodology are counting processes, martingales and stochastic integrals. This methodology allows for the analysis of timetoevent data which are more complex than composite endpoints and will be the topic of this course. The relevance of these methods is, e.g, illustrated in the current debate on how to analyse adverse events. Time permitting, we will also discuss connections between causal modelling and event histories.

Time Series Analysis
In many application areas, the data to be analyzed form a sequence of observations given at a sequence of time points, that is, a time series. For instance, stock prices, exchange rates or meteorological data are typically recorded at a sequence of time points and thus yield time series. The fact that the data are subject to a certain chronological order is crucial for their analysis and has to be taken into account when formulating statistical models. Trends, seasonal effects, and stationarity will be fundamental notions in this course. We will discuss autocovariance and autocorrelation functions as a tool for analyzing dependencies in time. Particular attention will be given to ARMA (auto regressive moving average) processes as the most important linear model for time series. Within the setting of ARMA processes we will discuss statistical inference and forecasting methods. In addition to problems on the mathematical theory, homework sets will include practical examples.

Topics in Insurance and Finance
The aim of the course is to discuss topics from the recent journal literature in the area of insurance and quantitative finance. The general focus of the course is on the differences and relations between finance and insurance. The lecture will in most parts be based on recent journal papers of which a list will be provided.
The contents of this course may change from year to year, depending on recent developments. Some examples of subjects are the following: Optimal Control Theory, allocation of risk capital, decision under uncertainty, risk measures, pricing in incomplete markets, pricing of insurance products.

Topics in Life and Pension Insurance
This lecture covers the following topics: Life and pension mathematics, the BlackScholesMerton model, unitlinked life and pension products (participating contracts and variable annuities), default risk modeling (structural approach) and optimal asset allocation and its application in life/pension insurance.

Valuation
The lecture introduces two main methods to estimate firm value: Marketbased approaches, such as multiples, and netpresent value approaches, such as discounted cash flows or valuation via CAPM. Further attention is given to relevant legal and institutional norms and special issues such as nonoperating assets or pensions and other liabilities. The theoretical knowledge is applied to case studies.
Further module descriptions depending on the chosen specialization
Specialization Financial Mathematics
Specialization Financial Economics
Specialization Actuarial Science