Introductory description

This module introduces the modelling techniques employed by actuaries. This module brings together a range of statistical techniques including stochastic processes, Markov chains, Survival models, estimation, maximum likelihood estimators and life tables to cover actuarial areas such as risk modelling, survival analysis and actuarial mathematics. It thus offers the opportunity to see how statistics is employed in an actuarial and thus authentic setting.

This module 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; or
  • ST228 Mathematical Methods for Statistics and Probability, and ST229 Probability for Mathematical Statistics, and ST230 Mathematical Statistics.

• Non-Statistics Students:

  • ST104 Statistical Laboratory and ST220 Introduction to Mathematical Statistics; or,
  • ST121 Statistical Laboratory. and ST232/ST233 Introduction to Mathematical Statistics.

• All students are advised to take ST333 Applied Stochastic Processes.

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.

This module covers the following actuarial areas:

• 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

Interdisciplinary

Students learn beyond the boundary of statistics and probability connecting their learning with the professional expectations of the chartered professional body dedicated to educating, developing and regulating actuaries based both in the UK and internationally.

Subject specific skills

• Demonstrate facility with mathematical, probabilistic and statistical methods.

• Select and apply appropriate mathematical and/or statistical techniques.

• Demonstrate knowledge of key mathematical and statistical concepts, both explicitly and by applying them to the solution of finance and financial problems.

• Create structured and coherent arguments communicating them in written form.

• Reason critically, carefully, and logically and derive judgements to support recommendations.

Transferable skills

• Problem solving: Use rational and logical reasoning to deduce appropriate and well-reasoned conclusions. Retain an open mind, optimistic of finding solutions, thinking laterally and creatively to look beyond the obvious. Know how to learn from failure.

• Self awareness: Reflect on learning, seeking feedback on and evaluating personal practices, strengths and opportunities for personal growth.

• Communication: Present arguments, knowledge and ideas, in a range of formats.

• Professionalism: Prepared to operate autonomously. Aware of how to be efficient and resilient. Manage priorities and time. Self-motivated, setting and achieving goals, prioritising tasks.