Prof Konstantinos Kardaras COL 6.07

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 Statistics with Finance. 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).

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.

20 hours of lectures and 10 hours of seminars in the LT. 3 hours of lectures and 1 hour of seminars in the ST.

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.

Compulsory written answers to two sets of problems.

S Ross, Stochastic Processes; R Norberg, Risk and Stochastics in Life Insurance; The Institute of Actuaries, Core reading Subject CT4. For full details of the syllabus of CT4, see http://stats.lse.ac.uk/angelos/guides/2004_CT4.pdf.

Exam (100%, duration: 3 hours) in the main exam period.