Week 10

Overview #

This week, we will finish Module 3 and cover the “in-scope” elements of Module 4:

• End of Section 3.4 (Module 3), covering the most complicated case of left-truncation and right-censoring (with parameters changing potentially with each claim)
• Calculating wihin layers for claim sizes (Module 3): reinsurance, and some policy transformations (in particular, stop loss / deductibles) lead to different “layers” of claims being covered by different parties. How do we calculate the distribution (or at least moments) of who pays what?
• Discretisation of continuous distributions (Module 4) - to be able to use Panjer, in particular; see next item)
• Use of Panjer’s recursion algorithm (Module 4), which allows us to calculate the exact compound distribution of any random sum, if the frequency follows the $(a,b)$ family
• Recap of the Normal approximation, as well as translated gamma and lognormal approximations, to be used when one needs a quick approximation, or when only moments are available (Module 4).

Module 3 maps into the detailed learning outcomes 1.1.2-1.1.4 and 1.1.6 of the CS2 syllabus here.

Module 4 is not part of the CS2 syllabus, but the “in-scope” elements must be covered for the Society of Actuaries CAE, exam ASTAM topic 2; see also here.

Main references and lectures #

Module 3: #

Read: Module 3 SLIDES

annotated slides (UG) | annotated slides (PG)

Watch: refer to your lecture recording under “Lecture Capture” ( UG/ PG). This is where annotated slides will be made available, too.

Module 4: #

Read: Module 4 SLIDES

annotated slides (UG) | annotated slides (PG)

Watch: refer to your lecture recording under “Lecture Capture” ( UG/ PG). This is where annotated slides will be made available, too.

Additional preparation and resources #

Mandatory #

1. Chapter 3.4 of Wuthrich (2023) (for Module 3)
2. Chapter 4.1.1-4.1.2, as well as 4.2.1 of Wuthrich (2023) (Module 4)

Optional #

1. n/a

Tutorials #

Note that a full list of exercises is available here. Please let us know of any mistake or required update on Ed.

Pre-Tutorial work #

Please study those questions before the tutorial.

Pre-Tutorial exercises are available in the Pre-Tutorial book, which already includes solutions. It is recommended to attempt the questions before looking at the solutions

Tutorial materials #

Some questions have been especially selected for the tutorials. Students should review and attempt those questions prior to their scheduled tutorial, after they complete the pre-tutorial work.

The Tutorial book includes all questions for the whole semester already, but solutions will only be added sequentially at the end of each week, as we work our way through the set.

Note that solutions will be gradually added to that same document. Hence it is not recommended to print it, as it will regularly change (typos will also dynamically be corrected).

This week #

This week, we will finish Module 3 and discuss Module 4, too.

Next week (week 11) #

Next week, tutorials will focus on Module 5.

Additional questions #

The “additional questions” are here for reinforcement or revision, but are not the main focus of the tutorials. Solutions for those exercises are already available.

Preparation for assessment #

Mid-semester (15%) and final (60%) exams #

Mid-semester exam is done! 😄

For the final exam:

• Finalise your Summary of Module 3.
• Start a Summary of Module 4

Assignment (25%) #

The Assignment is done! 😄

References #