ST227      Half Unit
Survival Models

This information is for the 2020/21 session.

Teacher responsible

Dr George Tzougas


This course is compulsory on the BSc in Actuarial Science. This course is available on the BSc in Business Mathematics and Statistics and BSc in Mathematics, Statistics and Business. This course is available as an outside option to students on other programmes where regulations permit and to General Course students.


Students must have completed Mathematical Methods (MA100) and Elementary Statistical Theory (ST102).

Course content

An introduction to stochastic processes with emphasis on life history analysis and actuarial applications. Principles of modelling; model selection, calibration, and testing; Stochastic processes and their classification into different types by time space, state space, and distributional properties; construction of stochastic processes from finite-dimensional distributions, processes with independent increments, Poisson processes and renewal processes and their applications in general insurance and risk theory, Markov processes, Markov chains and their applications in life insurance and general insurance, extensions to more general intensity-driven processes, counting processes, semi-Markov processes, stationary distributions. Determining transition probabilities and other conditional probabilities and expected values; Integral expressions, Kolmogorov differential equations, numerical solutions, simulation techniques. Survival models - the random life length approach and the Markov chain approach; survival function, conditional survival function, mortality intensity, some commonly used mortality laws. Statistical inference for life history data; Maximum likelihood estimation for parametric models, non-parametric methods (Kaplan-Meier and Nelson-Aalen), regression models for intensities including the semi-parametric Cox model and partial likelihood estimation; Various forms of censoring; The technique of occurrence-exposure rates and analytic graduation; Impact of the censoring scheme on the distribution of the estimators; Confidence regions and hypothesis testing.



This course will be delivered through a combination of classes and lectures totalling a minimum of 35 hours across  Lent Term. This year, some or all of this teaching may be delivered through a combination of virtual classes and flipped-lectures delivered as short online videos. This course includes a reading week in Week 6 of Michaelmas/Lent Term.

Students on this course will have a reading week in week 6 where they will be given review exercises to work on based on the first 5 weeks of the course. Also, students will be given a 10% coursework in R to work on within 24 hours in week 11 based on the material covered in the computer workshops which will run in weeks 5,7,8,9 and 10.

Formative coursework

Compulsory written answers to two sets of problems.

Indicative reading

S Ross, Stochastic Processes; R Norberg, Risk and Stochastics in Life Insurance; The Institute of Actuaries, CS2: Risk Modelling and Survival Analysis. For full details of the syllabus of CT4, see


Exam (90%, duration: 3 hours) in the summer exam period.
Coursework (10%) in the LT Week 11.

Student performance results

(2017/18 - 2019/20 combined)

Classification % of students
First 77.2
2:1 11.8
2:2 4.1
Third 1
Fail 5.9

Important information in response to COVID-19

Please note that during 2020/21 academic year some variation to teaching and learning activities may be required to respond to changes in public health advice and/or to account for the situation of students in attendance on campus and those studying online during the early part of the academic year. For assessment, this may involve changes to mode of delivery and/or the format or weighting of assessments. Changes will only be made if required and students will be notified about any changes to teaching or assessment plans at the earliest opportunity.

Key facts

Department: Statistics

Total students 2019/20: 172

Average class size 2019/20: 35

Capped 2019/20: No

Value: Half Unit

Guidelines for interpreting course guide information

Personal development skills

  • Leadership
  • Team working
  • Problem solving
  • Application of numeracy skills
  • Specialist skills