Published July 1, 2020 10:13 PM

You can find the text for the Home Exam Spring 2020 and a suggested solution in "lecture notes".

Everybody who handed in the exam has passed, a majority over 60% well done! I hope you enjoyed the course and learned a lot about life insurance! Have a good summer and good luck!

Published May 28, 2020 3:10 PM

I have uploaded a new version of the solution to the assignment. I just changed the values in table 2, page 11 (and also the code).

Also, Gjensidige is looking for an analyst and they are also interested in mater students. This may be interesting for you:


Published May 20, 2020 2:21 PM

I have uploaded some lecture notes for pricing of bonds that you can download here or by going to lecture notes. You do not need to study everything, just check the formulas for the case of Vasicek model. I have uploaded suggested solutions for the final exercise list 11, here.

The home exam will consist of two main exercises with several items. Problem 1 has 5 items and Problem 2 has 4 items. All items are worth 1 point except for the very last one which is worth 2 points, summing up a total of 10 points. Given the Corona situation, you need a regular E to pass, which means 4 points out of 10. In the exam, it is important that you explain how you arrive to the results, not only by providing the R-code, but also the...

Published May 12, 2020 11:25 AM

You can find some suggested solutions for List 10 here.

Next week I will upload some suggested solutions for Exercise List 11, which is the very last one, and some tips for the exam.

Published May 7, 2020 2:34 PM

For de som kan være interessert, er det nå utlyst en ledig fast stilling som statistiker ved Ahus

Published May 5, 2020 1:30 PM

You can find two suggested solutions for Exercise 1 and 3 from List 9 here.

Next week I will upload some suggested solutions for Exercise List 10.

Published Apr. 29, 2020 4:10 PM

I have uploaded the last exercise list 11 and suggested solutions for list 8. Next week, I will provide some solutions to list 9.

Published Apr. 21, 2020 1:33 PM

I have uploaded a suggested solution for the assignment in discrete time, and an extra solution for Exercise 2 in the assignment in continuous time. You will also find the corresponding R-codes in case you need them.

I have also uploaded the solutions for the Exercise List 7. Next week, I will upload Exercise List 11 (last one) and solutions for List 8. The home exam will be similar to an assignment (but divided into two exercises). Please, read carefully, try to solve at least two exercises from each list, and send me an e-mail if you have any do...

Published Apr. 14, 2020 6:41 PM

I hope you had a great cabin-free Easter holidays!

You can find the last chapter of this course here on stochastic interest rates. More suggested solutions to some selected exercises will come next week.

Remember the deadline for the assignment, this Thursday at 14:30!

Published Mar. 30, 2020 10:17 AM

The Faculty of Mathematics and Natural Sciences has finally decided that there will be no written ordinary school exams Spring 2020. Instead, there will be a "home exam" with grades pass/fail (bestått/ ikke bestått). This exam is for you to solve at home and hand in online. The exam will be made public when the original exam should have started (that is 11th of June) and it will last for 7 days. Think of this exam as a kind of mandatory assignment, just a bit more serious :-) In order to guarantee anonymity, Inspera will be used for uploading the papers.

You can read more information about the decision from the faculty by clicking here.

About the course: I have uploaded the lecture notes corresponding to Chapter 9: Unit-linked policies. Please read carefully. Also, I have uploaded Exer...

Published Mar. 24, 2020 3:15 PM

I have uploaded the new lecture for this week on Hattendorff's theorem and the solutions to two of the three problems from List 5. This week we will wait with List 7, so the homework is: if you have not tried any of the problems from List 5 or 6, you may do so this week! Also, remember the assignment! In the event that the exam is a "home exam" (which we still do not know), solving the entire assignment would be a really good traning! Remember to hand in the programme code you use in the assignment. Good luck!

Published Mar. 17, 2020 11:11 AM

I hope you are doing well, I hope we can meet again soon.

I have uploaded today's lecture. You can find it here. Probably, I would not have been able to go through everything in a regular lecture, but you can try to read everything at your own tempo. Also, try to solve the exercises from List 5 and List 6. At least one of each this week. You can send me questions or computations. NB: Some typos and miscalculations where found by a student in the lecture notes 4 and 7, and solution for Exercise 1 in List 4. All these have been corrected and reuploaded. Thanks!

There is possibility for video meetings, we can arrange...

Published Mar. 13, 2020 12:50 PM

As you probably know, the university is closed. This implies that all teaching and contact happens via internet. Here comes some information about how we will proceed.

  • Sections: I will create sections for each type of material in the menu to the left. Lecture notes, exercises (with some solutions inside the section), assignment, data, etc.
  • Assignment: the assignment must still be handed in on Canvas. Remember the deadline 16th of April at 14:30.
  • Exam: how the examination will be, when and how is still under evaluation. It is not upto us at this point. I will tell you as soon as we are informed about it.


1) Lecture notes: I am working on making lecture notes. This takes time, as I have to adapt the ones I use in the classroom and transfer them into LaTeX. But I plan on uploading some material already today. Please, be patient.

2) Exercises:...

Published Mar. 11, 2020 8:17 PM

The Department of Mathematics has cancelled all classroom lectures, at least, until the 14th of April. Please, check the course page regularly for updates.

If you have questions about the mandatory assignment or exercises, please contact me via e-mail.

I will upload material to the course page (lectures, exercises and some selected suggested solutions). Please contact me if you have questions when reading the material.

It is still undecided what will happen with examinations, so please, keep checking the course page for the latest updates.

Published Feb. 28, 2020 11:18 AM

As I commented to you some weeks ago, Gjensidige has two open internships. The application is now open. You can see the announcement following this link:

Published Feb. 27, 2020 3:22 PM

Exercise list 4 is available here or under Exercises. We continue next week with a review of the formulas for reserving and an example. We will also see Thiele's equations for reserving.

Published Feb. 22, 2020 3:37 PM

The mandatory assignment is available under "Exercises" or here. It consists of 4 exercises, you must do 2 of them or Exercise 2. You can already do Exercise 1 and part of Exercise 4. Also, you can try to do Exercise 2 with the formulas from our last lecture or following Example 4.8.1 from the book. 

The assignment has to be handed in online by logging in Canvas here and clicking on "Assignments". The deadline is 16th of April at 14:30. Notice that after this time, it will not be possible to upload any files. Good luck!

We continue on Tuesday solving exercises from the list 2 and 3. If time permits, I will review the theory on formulae for reserves again.

Published Feb. 18, 2020 8:19 PM

You can now download exercise list 3 here. You can solve all exercises except from exercise 3 in list 3.

In the next lecture we will solve exercises from list 2 (and maybe 3). Please, try to solve them. For exercise 1 in list 2, use a numerical method to solve the differential equation, e.g. Euler's method, Runge-Kutta method or Taylor's method.

Have a nice week! 

Published Feb. 13, 2020 2:53 PM

You can find the second exercise list here. You can do exercise 1, 2 and 3. Try to do Exercise 3. You can find the data here.

We continue on Tuesday with the review of the Lebesgue-Stieltjes integral and then how to compute prospective reserves and present values.

Published Jan. 28, 2020 4:55 PM

I uploaded an exercise list for you to solve some problems. You can download it here or find it in section: Exercises. I will solve some of them in the next lecture. We will then start a new topic on modelling of interest rates with some models from very simple ones to more sofisticated ones. The modelling of interest rates is highly important in life insurance, since one needs to compute present values of future cash-flows (with respect to (stochastic) interest rates, which will be the next topic.

Published Jan. 27, 2020 3:19 PM

Gjensidige is a Norwegian insurance company. They will announce an intership soon (12th of February) which you can already find by clicking here. The project is focused on the estimation of reserves for claims that have occured and/or been reported but are not yet settled. Their target is to use machine learning techniques, or classical techniques from statistics to estimate such payments and compare the two of them using real data. Therefore, they seek students with a bachelor's degree or in their master's degree in mathematics and/or statistics. There is also the possibility to summarize the findings of this actuarial problem into a master thesis for those who have not yet written it.

Published Jan. 14, 2020 3:15 PM

The course language will be English. The deadline for the first assignment is 16th of April at 14:30. The student representatives are: Anne Sofie Haag annesosh (at) and Jonas Augdal jonasaugdal (at)

We had a short overview of the content of the course (general insurance, calculation of premium reserves, distribution of reserves, etc.) and started a crash course on stochastic calculus and probability (probability space, random variables, convergence) that we will continue next week. Next Tuesday: Convergence, integration w.r.t. P, law, distribution, density, pushforward measure and integration w.r.t. pushforward measure, the concept of conditional and martingale). Meaning of martingality in finance and insurance. Markov processes.


Published Jan. 10, 2020 3:48 PM

The first lecture takes places in the mathematics building, room 108 (ground floor). We start with an introduction of the content of the course and useful results/definitions on probability that are important in the course. If you need a review on basic concepts this is a good opportunity!

Have a nice weekend,


Published Jan. 3, 2020 2:29 PM

Happy new year and welcome to STK4500!

Our first lecture will take place on the 14th of January at 12:15 pm in "Seminarrom 123" in Vilhelm Bjernes' hus (the building next to the department of mathematics).

The language of the course will be English unless everybody understands Norwegian, in such case it will be Norwegian. In any case, you may hand in your assignments and exam in English or any other Scandinavian language.

We will use the following supporting books for this course:

1. Michael Koller: Stochastic Models in Life Insurance. Springer (2012).

As supplementary book we may use:

2. Thomas Møller, Mogens Steffensen: Market-Valuation Methods in Life and Pension Insurance. Cambridge University Press (2007).


We plan to cover the following chapters from the book by Michael Koller:

1. General Life Insurance Model (a general introduction)...