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Enterprise Risk Management, 15 Credits

Swedish name: Riskbaserad portfölj- och företagsstyrning

This syllabus is valid: 2017-08-21 and until further notice

Course code: 5MA179

Credit points: 15

Education level: Second cycle

Main Field of Study and progress level: Mathematics: Second cycle, has second-cycle course/s as entry requirements

Grading scale: TH teknisk betygsskala

Established by: Faculty Board of Science and Technology, 2017-06-12


This course aims to provide knowledge in both the theoretical foundation and the practical application of quantitative methods used in finance and insurance, such as portfolio selection, investment strategies and the assessment of risk.

The course begins with an introduction to risk modeling and reserving in non-life insurance, with a focus on loss distributions and dependence modeling. Next, statistical properties of financial time series are studied together with one- and multidimensional models of these series and the definition and calculation of risk measures. Thereafter, risks and the effect of investment strategies for a life insurance company are studied with the help of simulation and stress testing. This includes implementing of a model of the life insurance company, where one of the earlier studied multi-dimensional models is used as a stochastic model for the relevant market variables. In this setting we also study interest rate sensitivity and immunization and how risk capital is calculated in accordance with the risk framework Solvency 2. Lastly, portfolio selection methods are studied. We start with classical Markowitz theory which we then generalize in different directions: taking liabilities into account, other return distributions and risk measures.

Expected learning outcomes

For a passing grade, the student must be able to:

Knowledge and understanding
  • thouroughly describe general risk management methods
  • define the various components of a market-consistent balance sheet for a life insurance company
  • explain the central concepts of risk modeling and reserving in non-life insurance                        
  • thouroughly describe fundamental results of survival theory.
Skills and abilities
  • analyse financial time series with respect to fundamental statistical properties
  • fit the most common loss distributions in non-life insurance to data
  • estimate and simulate single and multi-dimensional models for financial variables
  • calculate risk measures using simulation and analytical methods
  • use population data to individually estimate and smooth mortality rates 
  • calculate risk capital and evaluate different investment strategies for a life insurance company using simulation and stress testing
  • apply the portfolio selection methods covered in the course

Judgement and approach
  • assess in which situations the methods of the course are unsuitable to use.

Required Knowledge

The course requires 90 ECTS and with at least 60 ECTS in main field of Mathematics and Mathematical Statistics and including courses in Financial Mathematics and Monte Carlo-methods and a basic course in mathematical statistics. Proficiency in English equivalent to Swedish upper secondary course English 5/A. Where the language of instruction is Swedish, applicants must prove proficiency in Swedish to the level required for basic eligibility for higher studies.

Form of instruction

The teaching takes the form of lectures and supervision. The students work with lab assignments pairwise or in small groups.

Examination modes

The course is assessed through written lab reports, written tests and a mandatory seminar. On the written lab reports and the written tests one of the following grades is awarded: Fail (U), Pass (3), Pass with merit (4), Pass with distinction (5). On the mandatory seminare one of the following grades i awarded Fail (U) and Pass (3). For the course as whole, one of the following grades is awarded: Fail (U), Pass (3), Pass with merit (4), Pass with distinction (5). To pass the course, all examinations have to been awarded with a passing grade. The grade on the course is a summary assessment of the results of the examination's various parts and is done according to the following model.
  • The lab reports are assessed separately and an average assessment is calculated
  • Of the four written test results, the three bests count. These are summed up and a summary assessement is made
  • The laboratory assessment and the written test result will then be weighted with 70% weight for the laboratory grade and 30% weight for the written test result and rounded to the nearest integer
A student who has been awarded a passing grade for the course cannot be reassessed for a higher grade. Students who do not pass a test or examination on the original date are given another date to retake the examination. A student who has sat two examinations for a course or a part of a course, without passing either examination, has the right to have another examiner appointed, provided there are no specific reasons for not doing so (Chapter 6, Section 22, HEO). The request for a new examiner is made to the Head of the Department of Mathematics and Mathematical Statistics. Examinations based on this course syllabus are guaranteed to be offered for two years after the date of the student's first registration for the course.

Credit transfer
All students have the right to have their previous education or equivalent, and  their working life experience evaluated for possible consideration in the corresponding education at Umeå university. Application forms should be adressed to Student services/Degree evaluation office. More information regarding credit transfer can be found on the student web pages of Umeå university,, and in the Higher Education Ordinance (chapter 6). If denied, the application can be appealed (as per the Higher Education Ordinance, chapter 12) to Överklagandenämnden för högskolan. This includes partially denied applications

Other regulations

In a degree, this course may not be included together with another course with a similar content. If unsure, students should ask the Director of Studies in Mathematics and Mathematical Statistics. The course can also be included in the subject area of computational science and engineering and in the subject area of mathematical statistics


Valid from: 2017 week 34

Risk and portfolio analysis : principles and methods
Hult Henrik, Lindskog Filip, Hammarlid Ola, Rehn Carl Johan
New York : Springer : cop. 2012 : xiii, 335 p. :
ISBN: 9781461441021
Search the University Library catalogue

Quantitative risk management : concepts, techniques and tools
McNeil Alexander J., Frey Rüdiger, Embrechts Paul
Revised edition. : Princeton : Princeton University Press : [2015] : xix, 699 pages :
ISBN: 9780691166278
Search the University Library catalogue

Danielsson Jon
Financial Risk Forecasting
John Wiley & Sons : 2011 : 400 s. :
ISBN: 9780470669433 (inb.)
Search the University Library catalogue

Glasserman Paul
Monte Carlo methods in financial engineering
New York : Springer : cop. 2004 : 596 s. :
ISBN: 0-387-00451-3 (alk. paper)
Search the University Library catalogue

Meucci Attilio
Risk and asset allocation [Elektronisk resurs]
Dordrecht : Springer-Verlag Berlin and Heidelberg GmbH & Co. KG : 2005. : 550 p. :
ISBN: 9783540279044
Search the University Library catalogue

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