# BSc Actuarial Science and Mathematics / Course details

Year of entry: 2022

## Course unit details:Actuarial Models 1

Unit code MATH39511 10 Level 3 Semester 1 Department of Mathematics No

### Overview

In actuarial science one often deals with objects that change randomly over time and a natural way to model such objects is via stochastic processes. Markov chains are a particular class of stochastic processes that provide a good balance between tractability and realism. This course unit gives an introduction to the theory of Markov chains with emphasis on applications to actuarial science. In addition classical actuarial methods for the estimation of mortality rates like the Poisson model and graduation are covered.

### Pre/co-requisites

Unit title Unit code Requirement type Description
Actuarial Insurance MATH20972 Pre-Requisite Compulsory

### Aims

The first aim is to provide a theoretical foundation of Markov chains and their applications to various areas of actuarial science. The second aim is to introduce some classical actuarial methods of estimating mortality.

### Learning outcomes

After following this course, students should be able to:

• Given a description in words of a particular application where things change randomly over time, construct a Markov chain that serves as a model for this application.
• Derive and/or compute probabilities, expectations and distributions associated with a Markov chain given a description of these quantities in words.
• Given some data of a Markov chain, estimate its transition intensities and probabilities via maximum likelihood.
• Use the census approximation in order to estimate mortality rates given census data.
• Carry out certain tests commonly used in practice in order to verify whether a given graduation of mortality rates is successful.

### Syllabus

Syllabus
---------
- Discrete time Markov chains: stochastic processes, transition probabilities, time homogeneity, limiting behaviour. [7]
- Markov jump processes: Kolmogorov forward equations, construction, holding times, estimation of transition rates. [10]
- Graduation: Poisson model, crude rates, exposed to risk, statistical tests. [5]

### Assessment methods

Method Weight
Other 20%
Written exam 80%

Other: hand in homework for a number of selected exercises, 20%

Examination: End of semester examination, 80%

### Feedback methods

Feedback tutorials will provide an opportunity for students' work to be discussed and provide feedback on their understanding.  Coursework also provides an opportunity for students to receive feedback.  Students can also get feedback on their understanding directly from the lecturer, for example during the lecturer's office hour.

There is no reccomended reading for this module

### Study hours

Scheduled activity hours
Lectures 11
Tutorials 11
Independent study hours
Independent study 78

### Teaching staff

Staff member Role
Jennifer Sexton Unit coordinator