Course materials Actuarial Models

This page will in combination with Blackboard provide online access to the course materials (lecture notes, example sheets, etc.) for the unit MATH3/69511 Actuarial Models. For any questions please contact the lecturer Ronnie Loeffen by e-mail or drop by my office Room 2.122 ATB (e.g. during my office hour, Monday 2.30-3.30) or approach after a live class.

Lecture notes

• Lecture notes for MATH3/69511: click here (This set of notes will only be updated if errors are spotted).
• For the R-script that simulates sample paths of a discrete time Markov chain, see here.
• Additional lecture notes for MATH69511 only: for the latest version, click here (Update 4/10/2022: comments related to Example 1 have now been added). Solutions to the exercises will appear on Blackboard as the semester progresses. Latest update contains solutions to the first five exercises; let me know if you cannot access them.

Videos

The videos are on the University's Video Portal and the associated slides for each week are put on Blackboard.

Week plans

The week plans for each week are put on Blackboard.

Coursework

• For MATH39511 the coursework will consist of one piece of homework to be handed in. The deadline to hand in the work is Friday 2 December. The coursework will be provided at least one week in advance of the deadline and counts for 20% of the final mark.
• For MATH69511 the coursework will consist of two pieces of homework to be handed in. The first piece of coursework is the same one as for MATH39511 and has the same deadline of Friday 2 December. The deadline to hand in the second piece of coursework is Tuesday 13 December. The second piece of coursework will also be provided at least one week in advance of the corresponding deadline. The coursework counts for 20% of the final mark with the first piece making up 2/3 of the coursework mark and the second piece 1/3.

Example Sheets

• Sheet 1 and Solutions
• Sheet 2 and Solutions
• Sheet 3 and Solutions
• Sheet 4 and Solutions
• Sheet 5 and Solutions
• Sheet 7 and Solutions
• Sheet 8
• Sheet 9

Feedback

Tutorials will provide an opportunity for students' work to be discussed and provide feedback on their understanding. Naturally, the coursework also provides an opportunity for students to receive feedback. Students can also get feedback on their understanding directly from the lecturer, for example during the lecturer's office hour.

Individual learning outcomes (ILOs)

• Given a description in words of a particular application where things change randomly over time, construct a Markov chain that serves as a model for this application.
• Derive and/or compute probabilities, expectations and distributions associated with a Markov chain given a description of these quantities in words.
• Given some data of a time homogeneous Markov chain, estimate its transition intensities and probabilities via maximum likelihood.
• Use the census approximation in order to estimate mortality rates given census data.
• Carry out certain tests commonly used in practice in order to verify whether a given graduation of mortality rates is successful.

• Compute expected present values of cash flows associated with a Markov chain or a life insurance policy given a description of such cash flows in words. (MATH69511 only)