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# Actuarial Modelling - MAN00018I

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• Department: The York Management School
• Module co-ordinator: Dr. Lewis Ramsden
• Credit value: 20 credits
• Credit level: I
• Academic year of delivery: 2021-22

## Module summary

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 will run

Occurrence Teaching period
A Spring Term 2021-22 to Summer Term 2021-22

## 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;

• 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

1. Principles of actuarial modelling
2. Markov chains
3. Markov processes
4. Survival models
5. Estimation procedures for lifetime distributions
6. Likelihood estimators for the transition densities in a Markov model
7. Binomial model of mortality
8. Estimation of transition densities depending on age
9. Testing crude estimates of transition densities for consistency and the process of graduation
10. Loss distributions, their probabilities and moments
11. Risk models involving frequency and severity distributions
12. The concept of ruin for a risk model
13. Techniques for analysing a delay triangle and projecting the ultimate position
14. Monte Carlo simulation techniques

## Assessment

Task Length % of module mark
Essay/coursework
2000 word Case Study
N/A 20
Online Exam -less than 24hrs (Centrally scheduled)
Actuarial Modelling
3 hours 80

None

### Reassessment

Task Length % of module mark
Online Exam - 24 hrs (Centrally scheduled)
Actuarial Modelling
N/A 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.