Risk modeling in finance and insurance, 15 credits

Contents

This course aims to provide knowledge in both the theoretical foundation and the practical application of quantitative methods used in finance and insurance.

The course begins with a study of the statistical properties of financial time series together with one- and multidimensional models that are used for analysing and simulating such series.

Thereafter, risk modelling in life and non-life insurance are studied. In this setting, among other things, risk measures, life length theory, interest rate sensitivity, and distributions for the number of events and their amounts are studied, as well as calculations of risk capital according to Solvens 2,and how risk capital is calculated in accordance with the risk framework Solvency 2. Finally, machine learning methods are applied on practical problems within finance and insurance.

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 an insurance company
• thoroughly explain the most common distributions 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 and simulate single and multi-dimensional models for financial variables
• fit the most common distributions in non-life insurance to data
• calculate risk measures using simulation and analytical methods
• use population data to individually estimate and smooth mortality rates
• independently estimate death probabilities from data
• calculate risk capital and evaluate different investment strategies for a life insurance company using simulation and stress testing

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 and Swedish equivalent 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 is 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.

Examiners may decide to deviate from the modes of assessment in the course syllabus. Individual adaption of modes of assessment must give due consideration to the student's needs. The adaption of modes of assessment must remain within the framework of the intended learning outcomes in the course syllabus. Students who require an adapted examination must submit a request to the department holding the course no later than 10 days before the examination. The examiner decides on the adaption of the examination, after which the student will be notified.

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, http://www.student.umu.se, 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.

Transitional provisions

In the event that the syllabus ceases to apply or undergoes major changes, students are guaranteed at least three examinations (including the regular examination opportunity) according to the regulations in the syllabus that the student was originally registered on for a period of a maximum of two years from the time that the previous syllabus ceased to apply or that the course ended.