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You can find a suggested solution to the final exam here or by going to "Exams" on the left menu.
I wish you all a good and safe summer!
You can find today's exam here.
Good luck and have a nice summer!
Please, join the waiting room ONLY if you need help or have a question. Otherwise, it is difficult to keep track of who needs help and who doesn't :) Also, if you feel you are waiting too long, send me an e-mail and I will let you in ASAP. You can also ask questions directly via e-mail.
Good luck!
There will be an open room for questions according to: /english/for-employees/support/studies/mn/exam/digital-lecturers-visit.html
The Zoom information for Thursday's exam is here below:
David Banos is inviting you to a scheduled Zoom meeting.
Topic: Home Exam STK4500 Life Insurance and Finance
Time: Jun 10, 2021 09:00 AM Amsterdam, Berlin, Rome, Stockholm, Vienna
Join Zoom Meeting
https://uio.zoom.us/j/63657770714?pwd=ZDdobFhWRDhlY2tUeERzNzQxbHI2Zz09
Meeting ID: 636 5777 0714
Passcode: 116369
Documentation on how to use Zoom can be found here:
/english/services/it/phone-chat-videoconf/zoom/
One tap mobile
+46844682488,,63657770714# Sweden
+46850500828,,63657770714# Sweden
Dial by your location
...
Direct link: https://uio.zoom.us/j/64446598720?pwd=QTcrZzRPOWFlcC9TMEFIRDlpWldyQT09
Meeting ID: 644 4659 8720
Password: 410374?
The exam will consist of 2 exercises and a total of 5 items (Exercise 1, (a), (b) and Exercise 2, (a), (b) and (c)). All items are worth the same with a total of 50 points. The grade is obtained multiplying by two this score and in case of boundary grades, an examination of the whole exam will be made.
You will need to program your own code for this exam, but you are allowed to use any code from the course page that you can find here and here as supplement or support to your code.
Please, when writing the exam, be clear, mathematically rigorous and structured. Show the procedure and formulas you are using. The program is just to compute the final values and plots. You still need to write down the whole expressions. Use a text editor (such as LaTeX or Word) but if you want to do it by hand, please write clearly and avoid crossing out. Remember to hand in the code you have programmed!
...In general, the following guidelines apply in courses at the Department of Mathematics:
- The examination lasts 4 hours. In addition, you will have an extra 30 minutes to scan and upload your PDF.
- All examination aids are allowed (e.g. books, online resources, scientific programming tools, etc.).
- It...
Direct link: https://uio.zoom.us/j/66263408855?pwd=Yk41bmh6Y2grTFVLOXkyb0JtMWcrQT09
Meeting ID: 662 6340 8855
Password: 225144?
Download last year's exam here or by going to "Exam".
The solution for the assignment is published along with the R-code I used (in the code, for some reason, I modelled the reserves in terms of age of the insured and not of the contract, this is just a "shift" of the variable). The solution to the assignment is an example of how you should solve the home exam.
Next week I will publish more information about the structure of the home exam and what needs to be handed in. I will also publish last year's home exam with its solution.
See you on Monday!
I am very sorry to cancel this lecture, but I am having a quite severe allergic reaction to seasonal pollen and I could not manage to stop it in time. I do not feel confident enough to give today's lecture with the same quality I offer you usually :P so we better cancel it/postpone it. I am very sorry for that, I will compensate with some extra lecture in the time to come.
Next: I will upload the solution for the assignment this week. We move today's lecture to next Monday (the last curricular lecture). As the exam is on the 10th of June, we have plenty of days to arrange today's lecture or book any other time for questions. For any questions, please send me an e-mail.
Homework: Use the three hour lecture from today to read and solve some exercises! :D
Next digital lecture: Monday 3rd of May, 12:15-15:00 in Zoom.
Update: New updated lecture notes with an example for the implicit method for solving Thiele's PDE and the section on stochastic interest rate, also with an example with stochastic interest rate solved by an implicit method.
Next lecture (16th): We will see an example for the implicit finite difference method to solve a PDE when interest rate is stochastic (pension insurance) and Hattendorff's theorem.
Homework: Program the explicit and implicit methods from Section 9.3 and apply some examples of your own. Read the lecture notes. Specially Section 10 and 11.
Direct link: https://uio.zoom.us/j/66497038284?pwd=NzVqK3hLMjFHM3hFSnU5aEhINWVxQT09
Meeting ID: 664 9703 8284
Password: 948002?
Next digital lecture: Monday 26th of April, 12:15-15:00 in Zoom.
Update: This week I haven't had time to prepare the lecture notes for Monday, they will arrive at some point before the lecture. It's been a bit hectic! But I am planning to start the part on stochastic interest rates, which is veeeery similar to Unit-linked, so this is a nice thing!
Next lecture (15th): We will see an example for the implicit finite difference method to solve a PDE and then start stochastic interest rates. Note that when rates are stochastic, prices of bonds are then stochastic too, so we will again exploit the pricing theory we learnt in Section 8.
Homework: Review theory and look at examples. Program the explicit and implicit methods from Section 9.3. Finally, remember that the assignment has deadline 26 of April at 2 pm.
Direct link: https://uio.zoom.us/j/65162201297?pwd=THZvbk9Ka0lHOGYrK1RjSUZ0Q004UT09
Meeting ID: 651 6220 1297
Password: 802423
Next digital lecture: Monday 19th of April, 12:15-15:00 in Zoom.
Update: Sorry for the delay with updating the lecture notes! These ones were tough to prepare. I have updated the lecture notes with a section on a couple of numerical schemes to solve Thiele's PDE. I have also now included a table of contents in the lecture notes. You also have the digital blackboard from Monday in "digital lectures".
Next lecture (14th): We will see Section 9.3: Numerical methods to solve Thiele's PDE and some examples. We will see also how easy is to include time-inhomogeneous variables when the numerical method is impleted. For example, varying interest rates, instead of the boring assumption of constant interest.
Homework: Read the lecture notes, maybe Section 9.2 (again) and Section 9.3. Try to implement the examples, o...
Direct link: https://uio.zoom.us/j/61377447354?pwd=dzM2dnVxKzZIYThwZlNDRlM5QUJJUT09
Meeting ID: 613 7744 7354
Password: 018037
Next digital lecture: Monday 12th of April, 12:15-15:00 in Zoom.
Update: I have updated the lecture notes. I have uploaded the digital blackboard from Monday in "digital lectures".
Next lecture (13th): We continue with Unit-linked policies, Section 9.2: Thiele's PDE for UL-policies.
Homework: Read the lecture notes, Section 9.2 and solve some exercises (or check solutions for List 9) and solve the assignment.
Direct link: https://uio.zoom.us/j/62413340039?pwd=RHJlZSs0WjJPQ09EWElpb2x3QXZ5UT09
Meeting ID: 624 1334 0039
Password: 964197?
Next digital lecture: Monday 29th of March, 12:15-15:00 in Zoom.
Update: I have updated the lecture notes. I have uploaded the digital blackboard from Monday in "digital lectures". NB: it is no longer in alphabetic order. I have uploaded the solutions of List 9. I have not uploaded any new list of exercises. Work on the existing ones and the exercises from the lecture notes.
Next lecture (12th): Unit-linked policies (policies that invest in risky assets like those we have seen in mathematical finance). The mathematical formulas and how to derive them and use them.
Homework: Read the lecture notes, Section 9, especially the first part: Section 9.1. If you want, you can start reading Section 9.2.
As I told you, updates arrive every week. Today the university has decided to close again. So, no physical teaching on Friday! This will last at least until 11th of April. Enjoy the roller coaster and stay safe! We continue digitally on Monday! (See previous message) :)
Summary of further teaching:
Next digital lecture: Monday 22nd of March, 12:15-15:00 in Zoom.
Next physical lecture: Friday 19th of March, 14:15-16:00 in Auditorium 4, Vilhelm Bjerknes' building (VB). The building next to the Department of Mathematics.
Update: I have updated the lecture notes. I have uploaded the digital blackboard from today in "digital lectures". NB: it is no longer in alphabetic order. I have uploaded a new list of exercises, List 9. You can still not do Exercise 3, wait for that one.
Next lecture (11th): We will start with one of the core parts of the course: Unit-linked policies (policies that invest in risky assets like those we have seen in mathematical finance). In order to price such policies we need the 1st fundamental theorem of asset pricing.
Homewo...
Summary of further teaching:
Digital lectures: Mondays 12:15-15:00 in Zoom.
Physical lectures: Fridays 14:15-16:00 in Auditorium 4, Vilhelm Bjerknes' building (VB). The building next to the Department of Mathematics.
Theory and examples will be given in the (official) digital lecture, while problems (either suggested by you or by me) will be solved in the physical lectures. Send e-mail with suggestions or comments.
Update: I have uploaded the lecture notes from today, and added a new part with so-called Unit-linked insurance policies. I have uploaded solutions to Exercise list 7 and 8.
Next lecture (10th): We will finish the second fundamental theorem of asset pricing and the theory on pricing of finantial options. We will look at an example or two. If time permits, we will introduce Unit-linked insurances.
...
We will have digital teachings on Mondays, from 12:15-15:00 as before, since this is the only time that suits everybody. Nevertheless, since we are (so far) allowed to, we can have two hour physical lectures at Blindern. In these lectures I would like to solve problems and answer questions (in particular, you can propose a problem). To find a suitable time, let us use doodle:
https://doodle.com/poll/inqk5qhrdu4uuacy?utm_source=poll&utm_medium=link
Go to the link above and choose ALL options that suit you. Please, mark those that are not the best but that could be fine.
The option that wins will be chosen!
Next lecture: I will upload new lectures notes today or tomorrow, please stay tuned. We will start a quick review on mathematical finance and pricing of financial options which can be nice even for those who know it! I have uploaded new exercise lists. Good luck and see you soon!
There's still available space for last minute attendants!
Today, I will solve a "random" selection of problems. Please, join and bring questions or suggestions! Physical lectures can be a good way to exchange questions, thoughts and socialize.
Important: keep long distance to other students and spread as much as you can in the auditorium! Thank you and welcome back! :)
The University of Oslo has opened for the possibility of teaching in small groups up to max 20 people. For this reason I introduce the following changes:
1) We go back to physical teaching. We start forthcoming Monday 1st of May at Vilhelm Bjerknes' building, Auditorium 2 at 12:15.
2) Digital teaching will continue, but, it will be moved to Tuesday 2nd of March 12:15-14:00. We will then choose together a suitable time for future digital lectures.
3) The first 20 students will be granted a place in the lecture. Please, reserve a spot for yourself following this link:
https://doodle.com/poll/gkqdwiivs7cft4s2?utm_source=poll&utm_medium=link
4) Note the following: digital teaching will be as before and Mondays will be mostly u...