Program description for the Master s Degree Program in Mathematics and Finance

Transcription

1 Program description for the Master s Degree Program in Mathematics and Finance : English: Master s Degree in Mathematics and Finance Norwegian, bokmål: Master i matematikk og finans Norwegian, nynorsk: Master i matematikk og finans Qualifications awarded: Master of Science in Mathematics and Finance. : The total work load of the of study is 120 ECTS. Learning outcome: The candidate Knowledge has solid knowledge within advanced themes in mathematics and statistics, including partial differential equations, stochastic differential equations, theory for numerical calculations and inference methods in statistics. has advanced competence in international finance, including theory for portfolios, pricing of derivates, CAMP- and index models, credit risk, efficient markets and hedge funds. har advanced knowledge within stochastic modeling of financial time series, volatility prediction, and analysis of market risk. has good knowledge about optimation models and their applications in economics and finance. Skills can formulate and analyze advanced stochastic models for financial time series can utilize stochastic models for risk quantification and prediction of risks. has good ming skills and can contribute to development of software solutions. can analyze advanced financial models, among others models for pricing of derivates and dealing of risks. can handle tasks that require a lot of data and computation. General Competence can use specialized tools and models from mathematics and statistics to analyze problems and issues within economy and finance. can contribute to research and development within mathematics and finance. 1

2 can utilize knowledge within mathematics and finance on other problems and issues within natural as well as political/humanistic sciences. can do research work on his/her own, and communicate the results within the framework and terminology of the field can make knowledge based considerations on general issues within the field and communicate these to the rest of the society. Admission requirements: Admission to the Master s degree in mathematics and finance requires a Bachelor's degree in mathematics and finance or another degree following a of study of at least three years, or similar education approved in accordance with the Norwegian Universities Act section 3-4. The education must contain a specialization i mathematics and statistics corresponding to at least 80 ECTS. In addition, exams in basic issues within economics are required. An average mark of "C" or better is required in the Bachelor's degree or similar basis of admission. Group of students aimed at The master s in mathematics and finance is meant for students who want to acquire the specialized knowledge in mathematics and statistics necessary to solve development tasks within finance, market risk analysis and other fields of economics. The study is also well suited for students that seek specialized competence within mathematical and statistical modeling. and teaching The master's contains mainly specialized courses in direction finance, including three advanced courses at Handelshøgskolen, BFE. These are BED-3042 Intermediate Finance, BED-3043 Advanced Finance and SOK-3006 Microeconomics. In mathematics, the course MAT-2202 Optimization Models focuses at modeling of problems in economics and finance, while the course MAT-3212 Stochastic Differential Equations treats advanced stochastic modeling of financial time series. Apart from this one gives a course in theoretical statistics (STA-2002) and a course in mathematics dealing with linear partial differential equations (MAT-3200), including Fokker-Plank (Black-Scholes) equations and their applications in finance. The last part of the master study is a half a year's work with a master's thesis. Here the students improve their competence through work with research or development projects involving usage of mathematics and statistics within issues from economic or political science. In the third semester the master's thesis is prepared, either through a project thesis (MAT-3230) of size at Department of mathematics and statistics, or through a correspondingly advanced course at Handelshøgskolen, i.e. SOK-3050 Advanced topics in economics. The course descriptions follow as attachments at the end of the document. 2

3 Program structure: 1. term MAT-2201 Numerical Methods 2. term MAT-2202 Optimization Models 3. term SOK-3006 Microeconomics STA-2002 Theoretical Statistics BED-3042 Intermediate Finance BED-3043 Advanced Finance MAT-3200 Mathematical Methods MAT-3212 Stochastics Differential Equations MAT-3230 Project Paper in Mathematics and Finance /SOK-3050 Advanced topics in economics 4. term MAT-3931 Master s Thesis in Mathematics and Finance Exam and evaluation: The courses in the are evaluated in different ways; written exam, oral exam, or written home assignment. The details of the way the courses are evaluated are contained in the course descriptions. Work practices: No work practice is demanded in this of study. s : The language of instruction is English and all of the syllabus material is in English. Examination questions The Master s thesis may also be written either in English or a Scandinavian Internationalization and student exchange: The Department of Mathematics and statistics is establishing arrangements for student exchange. Other rules: Utfyllende bestemmelser for 2-årig master ved NT-fak which are being revised and will be processed at NT-fak in the fall The study will be evaluated every year. Each course will be evaluated at least every three times when it is given. Course evaluation consists of the assessments by the students and the course teacher(s). An overview of which courses that is to be evaluated each semester is to be found on the web pages of the faculty in question. 3

4 : The reading will be available. Demands for the master s thesis: The master s thesis MAT-3931 Master s Degree Thesis in Mathematics and Finance has a work load of 30 ECTS and is written in one semester. The thesis is normally written individually, but it is possible to finish the master thesis as a part of a group work. The master thesis is graded by a letter grade A F. The grade scale is used according to definitions and guidelines worked out by the national councils for the fields in question. 4

5 Attachment Course description: Compulsory courses: Numerical Methods MAT-2201 The course is mandatory in the Master's degree in industrial mathematics, and is included in the Bachelor's degree in mathematics and statistics. It also may be taken independent of study. MAT-1003 Calculus 3, MAT-1004 Linear algebra This course gives an introduction to basic concepts and issues of numerical computation. The topics treated include: Binary representation and floating point numbers, round-off errors, conditioning, rates of convergence, truncation and discretization errors, best approximation, numerical stability, and complexity analysis. Selected methods will be covered for some of these classes of problems: Linear systems of equations, nonlinear equations, overdetermined linear systems, numerical differentiation and integration, and numerical solution of differential equations. The students are expected to be able to utilize basic techniques and concepts in numerical computation. Among these are: Binary representation and floating point numbers, round-off errors, conditioning, rates of convergence, truncation and discretization errors, best approximation, numerical stability, complexity analysis, and generation of random numbers. In particular the students are expected to be able to use these techniques and concepts in linear algebra, numerical differentiation and integration, and differential equations. Written final exam of 4 hours duration. Letter grades (A-F). Section 22. Access to re-sit examinations Students who do not pass the previous ordinary examination, and who have the right to study the of study or course in question, can gain access to a resit examination in the event that the faculty has determined that re-sit examinations will be available for the course in question. Three mandatory homework sets. A passing grade is required on the mandatory homework sets for permission to take the exam. Optimization Models MAT-2202 The course is mandatory in the Bachelor s degree in mathematics and statistics and in the Master s degree in mathematics and finance. It also may be taken independent of study. MAT-1002 Calculus 2, MAT-1004 Linear algebra The main objective of this course is to learn to model problems in business, economics and the natural sciences as maximum or minimum problems. Linear ming models, the elementary part of their theory and a description of the main methods for solving them will form the core of the course. Some other types of optimization models will be outlined, and methods used to solve them will be described. 5

6 Students should be able to develop optimization models and solve them on a computer. They must have a basic understanding of both the methods of solving these problems and linear ming. In addition they should learn and be able to apply some of the most important methods for none-linear optimization. Written final exam of 4 hours duration. Letter grades (A-F). Section 22. Access to re-sit examinations Students who do not pass the previous ordinary examination, and who have the right to study the of study or course in question, can gain access to a resit examination in the event that the faculty has determined that re-sit examinations will be available for the course in question. A passing grade is required on the mandatory homework sets for permission to take the exam. Mathematical Methods MAT-3200 The course is included in the Master's degree in mathematics and in the Master's degree in industrial mathematics. It also may be taken independent of study upon approval of the Department of mathematics and statistics. MAT-2200 Differential Equations, MAT-2201 Numerical Methods This is a course on the mathematical modeling of linear continuous systems. These are systems containing an infinite number of degrees of freedom. Examples taken from the modeling of traffic flow, heat conduction, waves and option pricing in economy (Blach Scholes formula). The course will cover both analytic and numerical methods and will give an introduction to the numerical solution of partial differential equations with emphasis on the basic model equations derived in the course. The course MAT-2200, Differential equations, is a prerequisite and some familiarity with numerical methods is highly. Some knowledge of physics would also be helpful. The course gives an introduction to theory and methods for solving linear partial differential equations. The simplest mathematical models for traffic flow, heat conduction, diffusion, waves and option pricing in finance (Black Scholes) are introduced and methods for solving the resulting equations are given. The course gives the students the ability to apply both traditional analytic solutions methods and also numerical methods. The numerical methods are mainly of finite difference type. Numerical projects form an integral part of the course. Written final exam of 4 hours duration. Letter grades (A-F). Section 22. Access to re-sit examinations Students who do not pass the previous ordinary examination, and who have the right to study the of study or course in question, can gain access to a resit examination in the event that the faculty has determined that re-sit examinations will be available for the course in question. 6

7 Stochastic Differential Equations MAT-3212 The course is mandatory in the Master s degree in mathematics and finance. It also may be taken independent of study. MAT-2200 Differential Equations, STA-2001 Stokastiske prosesser The course is aimed at students with interests in stochastic modeling in finance and physics. It covers stochastic differential equations, including Itô¹s formula, Fokker-Planck equations and applications to mathematical finance. In addition, some of the following topics will be covered: Randomness in dynamical systems, self-similar and multi-fractal processes, stochastic differential equations driven by fractional noise, Lévy processes and jump-diffusions, elements of turbulence theory, and stochastic climate modeling. The students will learn to model dynamical phenomena in terms of differential equations that include stochastic terms, and to obtain analytical solutions of simple stochastic differential equations using Itô calculus. In addition, they will obtain some knowledge of advanced topics in stochastic processes, such as Lévy processes and multifractals. Oral exam. Letter grades (A-F). A passing grade is required on the mandatory homework sets for permission to take the exam. Theoretical Statistics STA-2002 The course is included in the Master's degree in industrial mathematics and in the Bachelor's degree in mathematics and statistics. It also may be taken independent of study. STA-1002 Probability and statistics 2 This course builds on STA-1001 Probability and statistics 1 with a thorough discussion of statistical methods and principles (sufficiency, power-optimality, exponential classes, maximum likelihood, Bayesian estimation). The aim of the course is to provide the students with a theoretical introduction to the general principles of statistical inference. Statistical inference concerns the problem of inferring properties and making decisions based on observed data and probability models. The students should be able to make use of the most important methods for data reduction, construction and evaluation of estimators and hypothesis tests under different models and situations. 7

8 Written final exam of 4 hours duration. Letter grades (A-F). Section 22. Access to re-sit examinations Students who do not pass the previous ordinary examination, and who have the right to study the of study or course in question, can gain access to a resit examination in the event that the faculty has determined that re-sit examinations will be available for the course in question. Three mandatory homework sets. A passing grade is required on the mandatory homework sets for permission to take the exam. Intermediate Finance BED-3042 The course can be taken as a master single topic. BED-2020 Investment and Finance Portfolio theory, basic derivative pricing in continuous time, CAPM and index models and the fixed income market. Students who have successfully completed the course should have achieved the following learning outcomes: Knowledge and comprehension: Knowledge of portfolio theory, basic derivative pricing in continuous time, CAPM and index models and the fixed income market Skills: Be able to explain important topics and derive results in portfolio theory, basic derivative pricing in continuous time, CAPM and index models and the fixed income market Advanced: Apply theoretical concepts and ideas to new areas Competence: The student should be able independently to develop their own competence and expertise in the field of portfolio theory, basic derivative pricing in continuous time, CAPM and index models and the fixed income market. Moreover, he or she should be able to discuss central questions, analyses and conclusions pertaining to these topics. The course has varied teaching methods. Written exam lasting 4 hours, comprising 100% of the final course grade (A-F). To access the exam, two submissions have been approved. English. Advanced Finance BED-3043 The course can be taken as a master single topic. 8

9 International finance, derivatives and credit risk, active management, efficient markets, behavioural finance, factor models and hedgefunds. Students who have successfully completed the course should have achieved the following learning outcomes: Knowledge and comprehension: Knowledge of international finance, derivatives and credit risk, active management, efficient markets, behavioural finance, factor models and hedgefunds. Skills: Be able to explain important topics and derive results in international finance, derivatives and credit risk, active management, efficient markets, behavioural finance, factor models and hedgefunds. Apply theoretical concepts and ideas to new areas Competence: The student should be able independently to develop their own competence and expertise in the field of international finance, derivatives and credit risk, active management, efficient markets, behavioural finance, factor models and hedgefunds. Moreover, he or she should be able to discuss central questions, analyses and conclusions pertaining to these topics. The course has varied teaching methods. Written exam lasting 4 hours, comprising 100% of the final course grade (A-F). A re-sit exam will be arranged for this course. To access the exam, three submissions have been approved. English. Project Paper in Mathematics and Finance MAT-3230 Project paper for master students in mathematics and finance only. Project paper for master students in mathematics and finance. The professional content will depend on the profile of the chosen paper. Contact the Department of Mathematics and Statistics. Mandatory, or can be replaced by SOK-3050 Advanced topics in economics The project paper gives the student knowledge of essential literature and methods relevant to the topic for the master thesis. It will give them basic field of expertise, and prepare the student to write the master thesis in mathematics and finance. Individual studies and supervision. The exam includes an individual project paper. Grades: Passed/failed. The project paper is written either in English or a Scandinavian 9

10 Advanced topics in economics SOK-3050 Theoretical subject. The reading list for this course is designed by each student individually under the guidance of an academic supervisor. The course will enable the student to independently acquire and utilize advanced economic analysis. Optional. Can replace MAT-3230 Project Paper in Mathematics and Finance Students who have successfully completed the course should have achieved the following learning outcomes: Knowledge and comprehension: knowledge of essential literature relevant to the topic for the master thesis Skills: The course should prepare the student to: write the master thesis in economics Competence: basic field of expertise The course has multiple teaching approaches. Term paper (100%). English. Master s Thesis in Mathematics and Finance MAT-3931 Master s thesis for master students in mathematics and finance only. 30 ECTS Thesis for master students in mathematics and finance. The professional content will depend on the field of study and the profile of the chosen thesis. Contact the Department of Mathematics and Statistics. Individual studies and supervision. The exam includes a master s thesis, an oral presentation of the thesis, and an oral exam. Letter grades (A-F). The Master's thesis is written either in English or a Scandinavian 10

11 Elective courses: Open Economy Macroeconomics SOK-3010 This course can be taken as a sigular course. The course includes the study of macroeconomic growth, short run macroeconomic fluctuations, unemployment and macroeconomic policy. Optional. The aim of the course is to give the student an understanding of macroeconomic analysis in the short and long term. The course has multiple teaching approaches. Written exam of 4 hours. Grades (A-F), F is failure. A re-sit exam will be arranged for this course. English. Computer-intensive Statistics STA-3001 The course is mandatory in the Master's degree in statistics and is included in the Master's degree in industrial mathematics. It may be taken independent of study upon approval of the Department of mathematics and statistics. STA-2001 Stochastic processes, STA-2002 Theoretical Statistics The course includes stochastic simulation, bootstrapping, Bayes theory, Laplace methods, the EM algorithm and Markov chain Monte Carlo (MCMC) techniques. The course is lectured in 5 parts. After each part the students must work independently with mandatory homework exercises. These must be approved to take the final exam, and the grades will be a part of the total evaluation. Optional. The aim of the course is to introduce students to modern computer based techniques for statistical inference. The students should get a good theoretical and practical knowledge of techniques for simulation of random variables, approximation of expected values, parameter estimation, resampling-based inference and Bayesian inference. The mandatory assignments should give the students experience in implementing and making use of these methods. Oral exam (50%) and approved mandatory homework sets (50%). Letter grades (A-F). A passing grade is required on the mandatory homework sets for permission to take the exam. 11

12 Multivariable Statistical Analysis STA-3002 The course is mandatory in the Master's degree in statistics and is included in the Master's degree in industrial mathematics. It may be taken independent of study upon approval of the Department of mathematics and statistics. STA-2002 Theoretical Statistics The course builds on STA-2002 Theoretical statistics and gives a thorough introduction to the multivariate normal distribution, as well as estimation of its parameters. The rest of the course gives a presentation of various areas in multivariable statistical analysis, such as the classification problem, testing of general linear hypotheses, principal component analysis, canonical correlation and factor analysis. Optional. The aim of the course is to introduce students to the basic principles for analyzing multivariate data based on the multinormal distribution and models based on multivariate correlations. By applying the multinormal distribution the students shall be able to do statistical inference for a wide range of situations, including one and multi-sample analysis and multiple regression analysis. The students will also be introduced to data reduction techniques, often used within a regression setting. Knowledge of techniques for classification problems and multiple comparisons is also expected. The mandatory assignments should give students practical experiences of multivariate analysis. Oral exam. Letter grades (A-F). A passing grade is required on the mandatory homework sets for permission to take the exam. 12