Actuarial Modelling - MAN00018I

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Professional requirements

This module covers part of the syllabus for the IFoA CM2 and CS2 modules.

Related modules

Additional information

Introduction to Probability and Statistics (MAT00004C) or an equivalent introductory probability module.

Module will run

Occurrence	Teaching period
A	Semester 2 2025-26

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

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 Loss distributions, their probabilities and moments Estimating unknown parameters for loss distributions Risk models involving frequency and severity distributions Reinsurance Ruin theory for risk models Claim reserving Survival models Estimation procedures for lifetime distributions Markov chains Estimation of transition probabilities Markov processes Likelihood estimators for the transition densities in a Markov model Binomial and Poisson model of mortality Census approximations Testing crude estimates of transition densities for consistency and the process of graduation

Indicative assessment

Task	% of module mark
Closed/in-person Exam (Centrally scheduled)	70
Essay/coursework	30

Special assessment rules

None

Indicative reassessment

Task	% of module mark
Closed/in-person Exam (Centrally scheduled)	70
Essay/coursework	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.

Indicative reading

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.