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The exam in STK4550 is in form of a final home exam !
Disclosure of exam assignment: June 2 at 2:30 PM
Submission deadline: June 9 at 2:30 PM
Examination system:
Inspera – see guides for digital exams
- The deadline (9. June, 14:30) for submission is 7 days (1 week) after the start time (2. June, 14:30), and the exam is delivered in Inspera. See how to anonymize your answers and submit your exam papers (in Norwegian).
- The expected extent of the work will be limited to 2 workdays, and all examination support materials are permitted. ...
Fasit oblig: Solutions, QQ-plotProb1, ME-plotProb1, QQ-plotProb2, RuinProbProb2
In our last (home) lessons (31. March and 2., 7. April) we studied different statistical methods of extreme value distributions, that is the block maxima method for both stationary and non-stationary data and the approach of Pickands-Balkema-de Haan (see Ch. 4 in the lecture notes or Ch. 6 in Embrechts).
This week we started with the discussion of the weak convergence of point processes which can be used to study extremal events from a more general and deeper point of view (see Ch. 5 in the lecture notes or in the book of Embrechts). The point process of exceedances, which counts the number of claim sizes over a certain threshold, is an example of a point process. The weak convergence of this process implies e.g. the distributional convergence of (normalized) maxima or order statistics of i.i.d. claim size variables.
Our goal in the coming lessons in April/May is to gain a solid understanding of the basic results of the theory of point processes....
The exam is run as a 7-day individual home exam with all aids allowed. The tasks will be similar to a mandatory task. Collaboration will not be considered cheating, but you must have formulated and written the answer that is submitted, and it should reflect your understanding of the syllabus. The grade will be pass/fail, and the limit for passing will be 40% (like E at the regular exam). The exam is published in Inspera at the original examination date and must be submitted as one PDF file in Inspera within the same time 7 days later. The faculty works on solutions for students who may not have access to a computer/network.
Note that the mandatory exercises are now available (see the message from 14. March below) !
Please, contact me via email (proske[at]math.uio.no), if you wish to discuss the lessons or other issues. Then we can also arrange Zoom meetings on an individual basis.
In our last lessons (3., 5., 10. and 12. March (online)) we discussed one of the main results of extreme value theory, that is the theorem of Fisher-Tippett-Gnedenko, which can be regarded as a central limit theorem for maximal claims (Ch. 3 in Embrechts). Further, we also started to address the problem of the characterization of the maximum domain of attraction of extreme value distributions by using methods from the theory of regularly varying functions.
In our next online or self-study lessons, 17./19. March (i.e. lecture notes online and Zoom meetings on an individual basis) we aim at finishing our discussion of the characterization of the different maximum domain of attractions.
Our study plan for the next weeks is the following:
24., 26., 31. March: Discussion of convergence rates with respect to the Fisher-Tippett-Gnedenko theorem and statistical methods for extreme value distributions (Ch. 3 and 6 in Embrechts).
April/May: Study...
Here: Mandatory assignment
Deadline: Thursday, 16. April, 14:30 (electronic submission).
Fra i morgen, torsdag 12. mars fram til 14. april, gis det ikke klasseromsundervisning ved instituttet. Ingen forelesninger, ingen gruppeundervisning, pga. koronasmitte.
Men vi skal fortsette med kurset, dvs. hver uke skal jeg legge ut beskjeder og forelesningsnotater/regne?velser til selvstudie.
Vi kan evt. ha Zoom-m?ter og diskutere progresjonen og sp?rsm?l fra deres side.
There will be no classroom lessons from 12. March until 14. April because of the corona virus epidemic.
However, we will continue with the course, that is every week I will post course information and lecture notes/exercises for the purpose of self-study on our website.
We can possibly arrange Zoom-meetings to discuss the learning progress and questions from you side.
In our last lessons (4./6., 11./13. and 18./20. February) we studied the exact asymptotics of ruin probabilities in the case of both large and small claim sizes (see Chapter 1 in the book of Embrechts). Further, we also discussed some basic results from the theory of regularly varying functions, which are useful for the analysis of heavy-tailed claim size distributions.
Next time (25./27. Feb.) we will start with Chapter 3 in the book of Embrechts, which is devoted to "central limit theorems" for maximal insurance claim sizes. The latter is important in the practical study of large claims, which may lead to the spontaneous ruin of an insurance company,
Solutions to Exercises 3 will be presented on Thursday, 27. Feb.
lecture notes: Part0, Part1, Part2, Part3, Part4, Part5, Part6, Part7, Part8, Part9, Part10, Part11, Part12, Part13
exercises: Exercises1, Exercises2, Exercises3, Exercises4, Exercises5, Exercises6, Exercises7, Exercises8, Exercises9, Exercises10
solutions: Ex1Prob12456, Ex1Prob3, Ex3, Ex4, Ex5, Ex6, Ex7, Ex8, Ex9
Studentrepresentanten for kurset er
Kristoffer Huertas (kehuerta[at]math.uio.no?)
Vi startet opp kurset (21. jan.) med en kort innf?ring i ekstremverdistatistikk og i teori av store avvik og fikk et oversikt over emner vi kommer til ? studere. Dessuten begynte vi (23./28. jan.) med ? repitere grunnleggende begrep og resultater fra sannsynlighetsregning (f.eks. (betinget) forventningsverdi, martingaler,...) som vi f.eks. trenger til estimering av ekstremverdi-fordelinger.
Neste gang (30. jan., 4./5. feb.) skal vi fortsette med kap. 1 i boken til Embrechts og studere effektene av "sm?" og "store" forsikringskrav p? modeller fra risikoteori.
Regne?velser kommer jeg til ? legge ut p? fagsiden neste uke.
In our first lesson (21. Jan.) I gave a brief introduction to extreme value theory and the theory of large deviations and an overview of some central problems we want to study in this course. Further, in our last lessons (23./28. Jan.), we finished our crash co...
Vi starter opp med kurset p? tirsdag, 21. januar, 10:15-12:00, VB Seminarrom 123 (dvs. det blir ikke (!) undervisning p? torsdag, 16. januar pga sykdom).
Our first lesson is supposed to be on Tuesday, 21. January, 10:15-12:00, VB Seminarrom 123 (so there is no (!) lesson on Thursday, 16. Jan. because of illness).
Vi starter opp med kurset p? torsdag, 16. januar, 10:15-12:00, VB Seminarrom 123 (det blir ikke (!) undervisning p? tirsdag, 14. januar pga sykdom).
Our first lesson is supposed to be on Thursday, 16. January, 10:15-12:00, VB Seminarrom 123 (there is no (!) lesson on Tuesday, 14. Jan.).
Vi skal bruke f?lgende pensumsb?ker i dette kurset:
1. P. Embrechts, C. Klüppelberg, T. Mikosch: Modelling Extremal Events: for Insurance and Finance. Springer (2012).
2. S.R.S. Varadhan: Large Deviations and Applications. Courant Institute of Mathematical Sciences (1994/2016).
St?ttelitteraturen vi trenger er:
3. A. McNeil, R. Frey, P. Embrechts: Quantitative Risk Management. Princeton Series in Finance (2015).
Pensum:
Det er planlagt ? gjennomg? f?lgende kapitler i boken til Embrechts, Klüppelberg, Mikosch om modellering av ekstreme hendelser:
1. Risk Theory (som innf?ring i sub-eksponentielle fordelinger)
2. Fluctuations of Sums
3. Fluctuations of Maxima
4. Fluctuations of Upper Order Statistics
5. An Approach to Extremes via Point Processes
6. Statistical Methods for Extremal Events
7. Time Series Analysis for Heavy-Tailed Processes (if time permits)
Vi skal ogs? ta gje...