Actuarial Modelling - MAN00018I
Module summary
The module aims to introduce a variety of models that are often used in an actuarial setting, as well as several techniques that are used to analyse these. Particular attention will be paid to their applications in an actuarial context.
The module provides opportunities for students to improve their skills in mathematical modelling of and abstracting from real-world phenomena.
Module will run
| Occurrence | Teaching period |
|---|---|
| A | Spring Term 2022-23 to Summer Term 2022-23 |
Module aims
The module aims to introduce a variety of models that are often used in an actuarial setting, as well as several of techniques that are used to analyse these. Particular attention will be paid to their applications in an actuarial context.
The module provides opportunities for students to improve their skills in mathematical modelling of and abstracting from real-world phenomena.
Module learning outcomes
After successful completion the student is able to:
Subject content
- explain the general principles of insurance modelling;
- explain the concepts and estimation methods of survival models, lifetime distributions, the Binomial model and models of state transfers;
- describe how to estimate transition intensities depending on age, exactly or using the census approximation;
- calculate probabilities and moments of loss distributions;
- construct risk models involving frequency and severity distributions;
- explain the concept of ruin for a risk model;
- describe and apply techniques for analysing a delay triangle and projecting the ultimate position;
- explain the concepts of Monte Carlo simulation;
Academic and graduate skills
- present analyses of various types of insurance contracts in a logical, rigorous, and concise way;
- strict logical reasoning from assumptions to conclusion;
- critically assess assumptions necessary to draw certain conclusions.
Module content
- Principles of actuarial modelling
- Markov chains
- Markov processes
- Survival models
- Estimation procedures for lifetime distributions
- Likelihood estimators for the transition densities in a Markov model
- Binomial model of mortality
- Estimation of transition densities depending on age
- Testing crude estimates of transition densities for consistency and the process of graduation
- Loss distributions, their probabilities and moments
- Risk models involving frequency and severity distributions
- The concept of ruin for a risk model
- Techniques for analysing a delay triangle and projecting the ultimate position
- Monte Carlo simulation techniques
Indicative assessment
| Task | % of module mark |
|---|---|
| Closed/in-person Exam (Centrally scheduled) | 80 |
| Essay/coursework | 20 |
Special assessment rules
None
Indicative reassessment
| Task | % of module mark |
|---|---|
| Closed/in-person Exam (Centrally scheduled) | 100 |
Module feedback
Students will receive feedback within one week of the hand-in problem sets. The feedback will be handed to students personally and takes the form of comments and suggestions for improvement written on the handed in work.
Indicative reading
- Macdonald A S, An Actuarial Survey of Statistical Models for Decrement and Transition Data, British Actuarial Journal 2 (1996),
- Brzezniak, Zdzislaw and Zastawniak, Tomasz, Basic stochastic processes; A course through exercises, Springer (1998)
- Bowers, Newton L; Gerber, Hans U; Hickman, James C; Jones, Donald A; Nesbitt, Cecil J., Actuarial mathematics, 2nd ed, Society of Actuaries, 1997.
- Hickman, James C., Introduction to actuarial modelling, North American Actuarial, Journal (1997) 1(3) 1-5.