Introductory description

This module runs in Term 2 and is available for students on a course where it is a listed option and as an Unusual Option to students who have completed the prerequisite modules.
Pre-requisites:
Statistics Students: ST218 Mathematical Statistics A AND ST219 Mathematical Statistics B
Non-Statistics Students: ST220 Introduction to Mathematical Statistics and ST104 Statistical Laboratory.

Results from this module may be partly used to determine exemption eligibility in the Institute and Faculty of Actuaries (IFoA) modules CS2 and CM1. (Independent application with the IFoA may be required to receive the exemption.)

Module web page

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

• Principles of actuarial modelling
• Principles of stochastic processes
• Markov chains and Markov jump processes
• Survival models: lifetimes, curtate future lifetime, expected value and variance.
• Estimation procedures for lifetime distributions: Kaplan—Meier estimate, Cox model
• Multi-state Markov models.
• Maximum likelihood estimators for transition intensities in multi-state models.
• Estimation in the Markov Model.
• Estimating mortality rates by age: exact methods, census approximations
• Process of graduation.
• Statistical tests for life tables.

Learning outcomes

By the end of the module, students should be able to:

• Describe the principles of actuarial modelling
• Describe the general principles of stochastic processes and their classification into different types.
• Define and apply a Markov chain.
• Define and apply a Markov jump process.
• Explain the concept of survival models.
• Describe estimation procedures for lifetime distributions
• Derive maximum likelihood estimators for the transition intensities in models of transfers between states with piecewise constant transition intensities.
• Describe the two-state model of a single decrement and compare its assumptions with those of the random lifetime model, derive maximum likelihood estimators for transition intensities and state the Poisson approximation to the estimator in the case of a single decrement.
• Describe how to estimate transition intensities depending on age, exactly or using the census approximation.
• Describe how to test crude estimates for consistency with a standard table or set of graduated estimates and describe the process of graduation.

Indicative reading list

View reading list on Talis Aspire

Subject specific skills

TBC

Transferable skills

TBC