Messages
You can find a suggested solution to the ordinary exam from December 2018 in "course material" or by clicking here. You did a very good exam! I hope you enjoyed the course and learned a lot of non-life insurance mathematics! Happy New Year!
I have prepared a list with some problems for our last lecture. You can download it here or by going to section "Course material".
This is a preliminary version. I recommend you to take a look and try to solve at least Problem 1 and 3.
See you on Friday!
You can find a suggested solution to the 2nd assignment in the section "course material" or by clicking here.
Comments and recommendations: The Norwegian fire losses was apparently quite hard to fit. The Pareto distribution was not a good fit as you may have noticed. In my solution I also justify that the exponential is not a good fit either (the Pareto is too risk-averse, while the exponential is too risky). I also include the premium using the empirical distribution (some students did that as well, very good!) I also tried a generalized Pareto. This one is indeed better, but not optimal. You may try to do your own inference :) For the exam: the important part of the assignment for the exam are items: (a), (e), (f), (g) and (i). Also the challenge. See you next Friday!
Next week there will be no lecture. Then we will have our last lecture on Friday the 16th of November. We will devote this lecture to the use of the Chain-Ladder method for estimating reserves. This is the most simple (and also used) method. We will see what it is based on and its restrictions. For this purpose I recommend you to take a look at the summary given in this paper.
The exam will most likely include a short question on this technique.
Comment about the assignment: Do not worry if you reject the hypothesis that the data comes from a Pareto distribution. Just continue with the analysis assuming so. You may also try to cut extreme values which actually are transfered to the reinsurance company and compute the premium based on observations below 100000nok. An alternative is to use the empirical density as underlying density for all possible claims....
Remember that we have no lecture tomorrow. We continue next week with Chapter 6. We will finish Chapter 6: Bühlmann and Bühlmann-Straub model and how to find the linear Bayes estimator (premium for a policy with past history). We will solve exercise list. After this lecture, we will go direct to the Chain ladder method for estimating reserves. Have a nice weekend!
You can find a suggested solution for the first assignment here.
Exercise 2 was maybe the most difficult since it contained some statistics from previous courses. I would like you to take a special look at Exercise 3 who very few managed to solve, and those who did used a rather complicated R-code. Panjer recursion is an important part of the course, hence worth having a look! :)
The student representatives for this course are:
Anne Birgitte Svindland, annebsv"att"math.uio.no
and
Aud B?rsting
aud.borsting"att"gmail.com
You can contact them for any questions, requests or comments regarding the subject.
I have uploaded a new version for the assignment with some corrections. Nothing important. I corrected some typos. Added a challenge in exercise (i) for those who would like to try it and I made exercise (j) more clear (it was not clear what distributions I wanted you to look at).
Try to solve as much as you can and hand in what you have done. I will solve the assignment during the lecture after you have handed in! Good luck and enjoy!
Hi! We will go back to room 819 and continue there, the blackboard has been replaced! We will start Chapter 6.
What is the idea behind? Usually, the Bayes estimator (minimizer of the quadratic risk) to price a policy is not easy to obtain, because the class we minimize the risk in is too large. In Chapter 6 we restrict this class to just linear functions, so the Bayes estimator will be the solution to a set of linear equations (normal equations). We will do this in an even more general setting than the heterogeneity model, which allows the policies have different distributions (the Bühlmann Model and the Bühlmann-Straub Model).
Important: As I am abroad on Friday 26th we will not have lecture this day. We may try to catch up later if necessary, but we have quite good time to finish C...
We will review and finish Chapter 5 on Bayes Estimation, then solve as many exercises from list 6 as possible. Remember the deadline for the first assignment is 11th of October.
You may download the exercise list 6 (Experience Rating) for the lectures for tomorrow here. We will solve some of these exercises next week.
Remember that the lecture on the 4th of October (tomorrow) is in room 107 on the ground floor.
You can find the exercise list 5 here. Also, a suggested solution for problem 5 from list 4 here.
We will continue on Friday with Chapter 5 and we will solve the problems from list 5. The teaching room is still to be announced, check before the lecture! (Hopefully the blackboard from the 8th floor is repaired but I have to check)
You can find the exercise list 4 here.
The next lecture will take place in Undervisningsrom 108!
The plan for the next lecture is to start Chapter 5 on Experience Rating. This is an important part of the course, as it generallizes the models we have seen so far. In this part of the course we take into account the past history of a single insurance policy. In order to do so, I will offer a gentle introduction on "Bayesian Statistics" and some elementary concepts which will be useful for Chapters 5 and 6.
We will then continue with the exercise list 4, and this will be the plan for the rest of the course. Next week we will solve exercises from the week before, as this was suggested by some students.
Remember to hand in the first assignment! The deadline is 11th of October at 14:30.
You can download exercise list 3 here. We will continue on Friday 21st of September at 12:15 in the Auditorium 5 in the building next to Niels Henrik Abels hus (Vilhelm Bjerknes hus). We will continue with Chapter 4 on bounds and asymptotics of the ruin and survival probabilities. We may start Chapter 5 on Experience Rating (which has not been taken into account so far) but this is not likely.
Norwegian Society for actuaries informs about the following coming conference in South Africa, that may be of interest to you!
Also, we have room for more participants in the Forsikringsseminar on the 25th of September at Hotel Bristol! Check this link for more information and registration.
I am travelling on Thursday and Friday to a workshop and for this reason I am forced to cancel this lecture (7/11/18). We resume again on friday the 14th of September. We will, as planned, start with Chapter 4 on "Ruin Theory".
Best regards,
David.
The exercise list 1 from last week can be downloaded here. Exercise list 2 from today here. The first assignment can be downloaded here.
The assignment can be handed in through "Devilry" whenever you want, but before the end of the semester.
Today Friday 31th of August, we finished chapter 2 and 3 on renewal process and Mixed Poisson process for N. We gave a storng law of large numbers and CLT for S when N is a renewal process. We saw some classical premia calculation principles and an exact method to compute the distribution of the claim amount process S (Panjer recursion scheme).
Next week we will start chapter 4 on Ruin Theory.
We will continue on Friday 27th at 12:15 p.m. in the room UE26.
You can find the information for each lecture here.
The temptative curriculum for the course is: (not every section in all chapters are included,but most of it).
Chapter 2: Models for the Claim Number Process (a rather quick review)
Chapter 3: The Total Claim Amount (Except section 3.2)
Chapter 4: Ruin Theory
Chapter 5: Bayes Estimation
Chapter 6: Linear Bayes Estimation
(if time permits) Chapter 11: Cluster Point Processes (except for last section)
I hope you all had a great summer holidays and are now ready for school start!
The course will most likely be taught in English as the syllabus is in English and we may expect some exchange students. Nevertheless, you may use Norwegian in your assignments, exams, questions, etc. if you so please.
The book we will use is: Non-Life Insurance Mathematics: An Introduction with the Poisson Process, Thomas Mikosch, Springer-Verlag Berlin Heidelberg 2009, 2nd Edition.
This course will focus on the mathematical aspects of the insurance world, therefore, a good background in analysis and probability theory is recommended. We will of course review some old stuff.
The first lecture is on Friday 24th of August, at 12:15 p.m. in the teaching room 819 (8th floor of Niels Henrik Abels hus).
We will start with some introduction in probability theory and modeling for the claim number pr...