F71MM - Markov Processes and Survival Modelling

Course leader(s):

• Damian Clancy (Edinburgh, January)

Syllabus

1. Stochastic processes with actuarial applications (1.1 1. Markov chains, 1.2 2. Poisson processes, 1.3 3.Markov processes , 1.4 4. Application to actuarial problems such as probability of ruin and mortality models)

2. Survival analysis and parameter estimation (2.1 1. Kaplan-Meier estimates, 2.2 2. The Cox model and likelihood functions, 2.3 3. Markov, binomial and Poisson models of mortality)

3. Graduation and forecasting (3.1 1. Graduation and tests of graduation, 3.2 2. Methods of mortality projection)

Learning outcomes

By the end of the course, students should be able to do the following:

• apply the Markov property in a variety of contexts, including mortality modelling.
• distinguish the long-term behaviour and stationarity of discrete and continuous-time Markov chains and apply Markov chain modelling in several problems, including solving equations for the stationary distribution.
• apply the different equivalent definitions and properties of Poisson processes to various applications involving probabilistic calculations.
• perform estimation of a survival distribution using methods including the Kaplan-Meier estimator and the Cox model.
• determine maximum likelihood estimators (with standard errors) in a Markov multi-state model and under the binomial and Poisson models.
• appraise the main methodologies for graduation and forecasting of observed mortality and morbidity rates.
• apply a range of appropriate statistical tests to check for adherence of a graduation to data.
• apply appropriate software tools in the computational aspects of Markov process and mortality modelling, including stochastic simulation, maximum likelihood estimation, graduation of observed rates and related tests, and forecasting.

Further details

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SCQF Level: 11

Credits: 15