## Actuarial Models 1

 Unit code: MATH39511 Credit Rating: 10 Unit level: Level 3 Teaching period(s): Semester 1 Offered by School of Mathematics Available as a free choice unit?: N

Prerequisite

#### 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.

#### 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.

#### 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 time homogeneous 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.

#### Assessment methods

• Other - 20%
• Written exam - 80%

#### Assessment Further Information

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

Examination: End of semester examination, two hours duration, 80%

#### Syllabus

Syllabus
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- 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]

Subject CT4, Models. Produced by the Actuarial Education Company.

#### 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.

#### Study hours

• Lectures - 22 hours
• Tutorials - 11 hours
• Independent study hours - 67 hours

#### Teaching staff

Ronnie Loeffen - Unit coordinator