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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: 2024-25

## 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 Semester 2 2024-25

## Module aims

The aim of this module is to introduce a variety of mathematical and statistical models that are often used to identify and quantify different risks, including techniques used for their analysis and implementation. In addition to the mathematical theory and reasoning underlying the models, students will also be given the opportunity to develop their computer programming skills and apply the models to real-world scenarios. Particular attention will be paid to the application of these models in an actuarial context, within general (non-life) and life insurance. This module covers part of the syllabus for the IFoA CM2 and CS2 modules.

## Module learning outcomes

After successful completion the student is able to:

Subject content

• explain the general principles of insurance risk modelling;

• calculate probabilities and moments of loss distributions;

• derive parameter estimates for loss distributions;

• construct risk models involving frequency and severity distributions;

• describe different reinsurance contracts;

• explain the concept of ruin for a risk model;

• describe and apply techniques for analysing a delay triangle and projecting outstanding reserves;explain the concepts and estimation methods of survival models and lifetime distributions;

• explain the concept of proportional hazard models;

• describe and construct Markov models for state transfer;estimate transition probabilities and intensities depending on age, exactly or using the census approximation;

• analyse a variety of models using computer programming software

• 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. Syllabus

2. Principles of actuarial modelling

3. Loss distributions, their probabilities and moments

4. Estimating unknown parameters for loss distributions

5. Risk models involving frequency and severity distributions

6. Reinsurance

7. Ruin theory for risk models

8. Claim reserving

9. Survival models

10. Estimation procedures for lifetime distributions

11. Markov chains

12. Estimation of transition probabilities

13. Markov processes

14. Likelihood estimators for the transition densities in a Markov model

15. Binomial and Poisson model of mortality

16. Census approximations

17. Testing crude estimates of transition densities for consistency and the process of graduation

## Assessment

Task Length % of module mark
Closed/in-person Exam (Centrally scheduled)
Actuarial Modelling closed exam
2.5 hours 70
Essay/coursework
Essay: Case Study
N/A 30

None

### Reassessment

Task Length % of module mark
Closed/in-person Exam (Centrally scheduled)
Actuarial Modelling closed exam
2.5 hours 70
Essay/coursework
Essay: Case Study
N/A 30

## Module feedback

Feedback will be given in accordance with the University Policy on feedback in the Guide to Assessment as well as in line with the School policy.

• Klugman, S.A., Panjer, H.H. and Willmot, G.E., 2012. Loss models: from data to decisions (Vol. 715). John Wiley & Sons.

Tse, Y.K., 2009. Nonlife actuarial models: theory, methods and evaluation. Cambridge University Press.

Kaas, R., Goovaerts, M., Dhaene, J. and Denuit, M., 2008. Modern actuarial risk theory: using R (Vol. 128). Springer Science & Business Media.

Bowers, Newton L; Gerber, Hans U; Hickman, James C; Jones, Donald A; Nesbitt, Cecil J., 1997. Actuarial mathematics, 2nd ed, Society of Actuaries.

Macdonald, A.S., Richards, S.J. and Currie, I.D., 2018. Modelling mortality with actuarial applications. Cambridge University Press.

The information on this page is indicative of the module that is currently on offer. The University is constantly exploring ways to enhance and improve its degree programmes and therefore reserves the right to make variations to the content and method of delivery of modules, and to discontinue modules, if such action is reasonably considered to be necessary by the University. Where appropriate, the University will notify and consult with affected students in advance about any changes that are required in line with the University's policy on the Approval of Modifications to Existing Taught Programmes of Study.