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.
Occurrence | Teaching period |
---|---|
A | Semester 2 2024-25 |
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.
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.
Syllabus
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
Task | % of module mark |
---|---|
Closed/in-person Exam (Centrally scheduled) | 70 |
Essay/coursework | 30 |
None
Task | % of module mark |
---|---|
Closed/in-person Exam (Centrally scheduled) | 70 |
Essay/coursework | 30 |
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.