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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



Additional Requirements

Please note.


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.


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:

  • Understand the basic theory of Markov chains.
  • Apply the theory of Markov chains to processes of actuarial interest.
  • Understand how Markov chains can be used to model various phenomena appearing in actuarial science.
  • Use some classical actuarial methods to estimate the force of mortality.
  • Perform tests to assess the goodness of fit of a graduation procedure.



Assessment methods

  • Other - 10%
  • Written exam - 90%

Assessment Further Information

Other: hand in homework for a number of selected exercises, 10%

Examination: End of semester examination, two hours duration, 90%


- 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]


Recommended reading

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 or in-class tests (where applicable) also provide 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

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