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- 3/27/12
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Hi,
I'm trying to figure out what courses to apply to for my masters. I have a BSc i engineering physics and would like to learn more about quantative risk management. I'm interested in statistiks but I'm not sure how much I'll need and if it would be wiser to learn more programing languages or more numerical analysis. The courses I'm thinking about right now are:
Stationary Stochastic Processes
Stochastic processes find applications in a wide variety of fields, and offer a refined and powerful framework to examine and analyze various signals. This course is aimed at introducing the basic theory of stochastic processes, as well as to show how the theory can find applications in a variety of fields.
NUMERICAL LINEAR ALGEBRA
The course is a follow-up to the basic course Linear Algebra. We teach how to solve practical problems using modern numerical methods and computers. Central concepts are convergence, stability, and complexity (how accurate the answer will be and how rapidly it is computed). Other tools include matrix factorization and orthogonalization. Algorithms covered can, among other things, be used to solve very large systems of linear equations that arise when discretizing partial differential equations, and to compute eigenvalues.
ECONOMIC AND FINANCIAL DECISION-MAKING
The goal for education at this level is to instil a deeper understanding of economic theory and the application of scientific methods of analysis. The objective is also to instil an ability to handle empirical material in an independent and critical manner. The more specific aims of this course are to enhance students’ understanding of situations where individuals, firms and organizations operate in environments characterized by risk, uncertainty and imperfect information.
TIME SERIES ANALYSIS
Practical and theoretical knowledge in modelling, estimation, validation, prediction, and interpolation of time discrete dynamical stochastic systems, mainly linear systems. The course also gives a basis for further studies of time series systems, e.g. Financial statistics and Non-linear systems.
NON-LINEAR DYNAMICAL SYSTEMS
Dynamical systems in discrete and continuous time. The fixed point theorem and Picard's theorem on the existence and uniqueness of solutions to ordinary differential equations. Phase space analysis and Poincare's geometrical methods. Local stability theory (Liapunov's method and Hartman-Grobman's theorem). The central manifold theorem. Basic local bifurcation theory. Global bifurcations and transition to chaos. Chaotic and strange attractors (dynamics, combinatorial description).
FINANCIAL VALUATION AND RISK MANAGEMENT
The course deals with three main topics: portfolio theory, measurement and management of credit risk, and measurement and management of financial risk. The objective of this course is to give the students an understanding and hands-on knowledge of basic methods within risk management. The course begins with MV-optimization with different constraints and stochastic dominance. Then follows measurement and control of credit risk, which are then applied to the Basel II rules. Finally, the course covers VaR (Value-at-Risk) and CVaR/ETL (Conditional Value-at-Risk/Expected Tail Loss), which are computed for different portfolios with and without derivatives using analytical and simulation based techniques.
INNOVATION MANAGEMENT
The course Innovation Management aims (1) to provide students with fundamental knowledge of the phenomenon of innovation and innovation processes from the perspective of firms and organizations, and (2) to enable students to use basic theoretical and practical tools to understand and handle real-world innovation processes; technology development and innovation strategy, such as strategies for product development (goods and services).
MONTE CARLO AND EMPIRICAL METHODS FOR STOCHASTIC INFERENCE
The purpose of the course is to give the students tools and knowledge to handle complex statistical problems and models. The aim is that students shall gain proficiency with such modern computer intencive statistical methods as are required in order to estimate and assess uncertainties in complex models that often arise in different applications (e.g. economics, biology, climate, environmental statistics). The main aim lies in enhancing the scope of statistical problems that the student will be able to solve.
STATISTICAL MODELLING OF EXTREME VALUES
The course aims to give theoretical knowledge in mathematical modelling of extreme events and discusses in detail how the theory can be applied in practice. Different courses of action for modelling of extreme values are discussed and guidance is given as to how the models can be modified to fit different practical situations. The students should also learn about more advanced models for extreme value analysis, including extreme values for non-stationary processes.
FINANCIAL ECONOMICS
The course contains the following building blocks
· investment decision under certainty: the risk free rate and Fisher-separability;
· risk aversion and expected utility;
· Arrow-Debreu securities;
· portfolio theory
· market equilibrium: CAPM and multi-factor equilibrium models;
· derivatives
· term structure of the interest rates;
· real options;
· efficient markets;
· information asymmetry and agent theory;
VALUATION OF DERIVATIVE ASSETS
The student should get a thorough understanding and insight in the economical and mathematical considerations which underlie the valuation of derivatives on financial markets. The student should get knowledge about and ability to handle the models and mathematical tools that are used in financial mathematics. The student should also get a thorough overview concerning the most important types of financial contracts used on the stock- and the interest rate markets and moreover get a solid base for understanding contracts that have not been explicitely treated in the course.
ECONOMICS, EMPIRICAL FINANCE
The course begins with a brief discussion of the estimation methods, such as Least Square (LS), Maximum Likelihood (ML) and Generalised Method of Moment (GMM), which is followed by a description of the time-series properties of various financial data. Thereafter, it gives a presentation of the most important theoretical models in finance that is accompanied by an explanation of the available methods for testing the theoretical hypotheses. The course concentrates on the following issues: tests for information efficiency, market microstructure, event study, portfolio valuation, tests for the asset pricing models and fixed incomes. There is a number of computer exercises which are supposed to give the students practical skills for solving econometric problems.
FINANCIAL STATISTICS
The course deals with model building and estimation in non-linear dynamic stochastic models for financial systems. The models can have continuous or discrete time and the model building concerns determining the model structure as well as estimating possible parameters. Common model classes are, e.g., GARCH models with discrete time or models based on stochastic differential equations in continuous time. The course participants will also meet statistical methods, such as Maximum-likelihood and (generalised) moment methods for parameter estimation, kernel estimation techniques, non-linear filters for filtering and prediction, and particle filter methods.
The course also discusses prediction, optimization, and risk evaluation for systems based on such descriptions.
NON-LINEAR TIME SERIES ANALYSIS
Different types of non-linear time series models. Non-parametric estimates of non-linearities, i.a. using kernel estimates. Identification of model structure using parametric and non-parametric methods, parameter estimation. State models for non-linear systems, filtering. Prediction in non-linear systems. Modelling using non-linear stochastic differential equations. Recursive methods for parameter estimation in non-stationary time series. Design of experiments for identification of dynamic systems.
Have I missed something or should I skip any course? Thinging about changing the numerical linear algebra to
MARKOV PROCESSES
Markov chains: model graphs, Markov property, transition probabilities, persistent and transient states, positive and null persistent states, communication, existence and uniqueness of stationary distribution, and calculation thereof, absorption times.
Poisson process: Law of small numbers, counting processes, event distance, non-homogeneous processes, diluting and super positioning, processes on general spaces.
Markov processes: transition intensities, time dynamic, existence and uniqueness of stationary distribution, and calculation thereof, birth-death processes, absorption times.
Introduction to renewal theory and regenerative processes.
any thoughts?
I'm trying to figure out what courses to apply to for my masters. I have a BSc i engineering physics and would like to learn more about quantative risk management. I'm interested in statistiks but I'm not sure how much I'll need and if it would be wiser to learn more programing languages or more numerical analysis. The courses I'm thinking about right now are:
Stationary Stochastic Processes
Stochastic processes find applications in a wide variety of fields, and offer a refined and powerful framework to examine and analyze various signals. This course is aimed at introducing the basic theory of stochastic processes, as well as to show how the theory can find applications in a variety of fields.
NUMERICAL LINEAR ALGEBRA
The course is a follow-up to the basic course Linear Algebra. We teach how to solve practical problems using modern numerical methods and computers. Central concepts are convergence, stability, and complexity (how accurate the answer will be and how rapidly it is computed). Other tools include matrix factorization and orthogonalization. Algorithms covered can, among other things, be used to solve very large systems of linear equations that arise when discretizing partial differential equations, and to compute eigenvalues.
ECONOMIC AND FINANCIAL DECISION-MAKING
The goal for education at this level is to instil a deeper understanding of economic theory and the application of scientific methods of analysis. The objective is also to instil an ability to handle empirical material in an independent and critical manner. The more specific aims of this course are to enhance students’ understanding of situations where individuals, firms and organizations operate in environments characterized by risk, uncertainty and imperfect information.
TIME SERIES ANALYSIS
Practical and theoretical knowledge in modelling, estimation, validation, prediction, and interpolation of time discrete dynamical stochastic systems, mainly linear systems. The course also gives a basis for further studies of time series systems, e.g. Financial statistics and Non-linear systems.
NON-LINEAR DYNAMICAL SYSTEMS
Dynamical systems in discrete and continuous time. The fixed point theorem and Picard's theorem on the existence and uniqueness of solutions to ordinary differential equations. Phase space analysis and Poincare's geometrical methods. Local stability theory (Liapunov's method and Hartman-Grobman's theorem). The central manifold theorem. Basic local bifurcation theory. Global bifurcations and transition to chaos. Chaotic and strange attractors (dynamics, combinatorial description).
FINANCIAL VALUATION AND RISK MANAGEMENT
The course deals with three main topics: portfolio theory, measurement and management of credit risk, and measurement and management of financial risk. The objective of this course is to give the students an understanding and hands-on knowledge of basic methods within risk management. The course begins with MV-optimization with different constraints and stochastic dominance. Then follows measurement and control of credit risk, which are then applied to the Basel II rules. Finally, the course covers VaR (Value-at-Risk) and CVaR/ETL (Conditional Value-at-Risk/Expected Tail Loss), which are computed for different portfolios with and without derivatives using analytical and simulation based techniques.
INNOVATION MANAGEMENT
The course Innovation Management aims (1) to provide students with fundamental knowledge of the phenomenon of innovation and innovation processes from the perspective of firms and organizations, and (2) to enable students to use basic theoretical and practical tools to understand and handle real-world innovation processes; technology development and innovation strategy, such as strategies for product development (goods and services).
MONTE CARLO AND EMPIRICAL METHODS FOR STOCHASTIC INFERENCE
The purpose of the course is to give the students tools and knowledge to handle complex statistical problems and models. The aim is that students shall gain proficiency with such modern computer intencive statistical methods as are required in order to estimate and assess uncertainties in complex models that often arise in different applications (e.g. economics, biology, climate, environmental statistics). The main aim lies in enhancing the scope of statistical problems that the student will be able to solve.
STATISTICAL MODELLING OF EXTREME VALUES
The course aims to give theoretical knowledge in mathematical modelling of extreme events and discusses in detail how the theory can be applied in practice. Different courses of action for modelling of extreme values are discussed and guidance is given as to how the models can be modified to fit different practical situations. The students should also learn about more advanced models for extreme value analysis, including extreme values for non-stationary processes.
FINANCIAL ECONOMICS
The course contains the following building blocks
· investment decision under certainty: the risk free rate and Fisher-separability;
· risk aversion and expected utility;
· Arrow-Debreu securities;
· portfolio theory
· market equilibrium: CAPM and multi-factor equilibrium models;
· derivatives
· term structure of the interest rates;
· real options;
· efficient markets;
· information asymmetry and agent theory;
VALUATION OF DERIVATIVE ASSETS
The student should get a thorough understanding and insight in the economical and mathematical considerations which underlie the valuation of derivatives on financial markets. The student should get knowledge about and ability to handle the models and mathematical tools that are used in financial mathematics. The student should also get a thorough overview concerning the most important types of financial contracts used on the stock- and the interest rate markets and moreover get a solid base for understanding contracts that have not been explicitely treated in the course.
ECONOMICS, EMPIRICAL FINANCE
The course begins with a brief discussion of the estimation methods, such as Least Square (LS), Maximum Likelihood (ML) and Generalised Method of Moment (GMM), which is followed by a description of the time-series properties of various financial data. Thereafter, it gives a presentation of the most important theoretical models in finance that is accompanied by an explanation of the available methods for testing the theoretical hypotheses. The course concentrates on the following issues: tests for information efficiency, market microstructure, event study, portfolio valuation, tests for the asset pricing models and fixed incomes. There is a number of computer exercises which are supposed to give the students practical skills for solving econometric problems.
FINANCIAL STATISTICS
The course deals with model building and estimation in non-linear dynamic stochastic models for financial systems. The models can have continuous or discrete time and the model building concerns determining the model structure as well as estimating possible parameters. Common model classes are, e.g., GARCH models with discrete time or models based on stochastic differential equations in continuous time. The course participants will also meet statistical methods, such as Maximum-likelihood and (generalised) moment methods for parameter estimation, kernel estimation techniques, non-linear filters for filtering and prediction, and particle filter methods.
The course also discusses prediction, optimization, and risk evaluation for systems based on such descriptions.
NON-LINEAR TIME SERIES ANALYSIS
Different types of non-linear time series models. Non-parametric estimates of non-linearities, i.a. using kernel estimates. Identification of model structure using parametric and non-parametric methods, parameter estimation. State models for non-linear systems, filtering. Prediction in non-linear systems. Modelling using non-linear stochastic differential equations. Recursive methods for parameter estimation in non-stationary time series. Design of experiments for identification of dynamic systems.
Have I missed something or should I skip any course? Thinging about changing the numerical linear algebra to
MARKOV PROCESSES
Markov chains: model graphs, Markov property, transition probabilities, persistent and transient states, positive and null persistent states, communication, existence and uniqueness of stationary distribution, and calculation thereof, absorption times.
Poisson process: Law of small numbers, counting processes, event distance, non-homogeneous processes, diluting and super positioning, processes on general spaces.
Markov processes: transition intensities, time dynamic, existence and uniqueness of stationary distribution, and calculation thereof, birth-death processes, absorption times.
Introduction to renewal theory and regenerative processes.
any thoughts?
