1. Be able to understand the differences between stochastic and deterministic modelling.
2. Explain the need of stochastic processes to model the actuarial data
3. Be able to perform model selection depending on the outcome from a model.
4. Prepare the students adequately and to develop their skills in order to be ready to sit for the exams of CT4 subject of the Institute of Actuaries.

(LO1) 1 Understand Use Markov processes to describe simple survival, sickness and marriage models, and describe other simple applications, Derive an appropriate Markov multi-state model for a system with multiple transfers, derive the likelihood function in a Markov multi-state model with data and use the likelihood function to estimate the parameters (with standard errors).

2 The Kaplan-Meier (or product limit) estimate, the Nelson-Aalen estimate , Describe the Cox model for proportional hazards Apply the chi-square test, the standardised deviations test, the cumulative deviation test, the sign test, the grouping of signs test, the serial correlation test to testing the adherence of graduation data.

3 Understand the connection between estimation of transition intensities and exposed to risk (central and initial exposed to risk) , Apply exact calculation of the central exposed to risk.

(LO3) Understand the connection between estimation of transition intensities and exposed to risk (central and initial exposed to risk). Apply exact calculation of the central exposed to risk

(LO4) Understand the time series together with its applications

(S2) Problem solving skills

(S3) Numeracy

(S4) Commercial awareness

1) Renewal processes : describe the distribution of the number of events in a given time interval and/or the distribution of inter-event times.

2) Mortality models : illustrate the usefulness of Markov chains in the modelling of mortality. Describe the Binomial model of the mortality of a group of identical individuals (subject to no other decrements between two given ages).

3) Survival, sickness, marriage and other simple models: described via/as applications of Markov processes. Derive Kolmogorov forward and backward equations for a Markov process with time independent and time/age dependent transition and solve them in simple cases.

4) Likelihood functions: describe the Cox model for proportional hazards and use the partial likelihood estimate (with standard errors) to estimate its parameters. Reduce the Binomial likelihood function to a function of a single parameter, under the assumption of uniform distribution of deaths or constant force of mortality, and estimate this single parameter.

5) 2-state models: derive the likelihood function for a 2-states model with states Alive and Dead , under Cox, Binomial and Poisson models.

6) Multi-state models: describe an appropriate Markov multi-state model for a system with multiple transfers, derive the likelihood function in a Markov multi-state model with data and use the likelihood function to estimate the parameters (with standard errors).

7) Comparison: describe the advantages and disadvantages of the multi-state model versus the Binomial model, including consistency, efficiency, simplicity of the estimators and their distributions.

8) Survival functions: estimate a survival function using the Kaplan-Meier or Nelson-Aalen method.

9) Statistical tests: explain statistical tests of crude estimates for comparing with a standard table:  chi-square test, standardised deviations test, cumulative deviation test, sign test, grouping of signs test and the serial cor relation test to testing the adherence of graduation data.

10) Exposed to risk: Connection between estimation of transition intensities and exposed to risk (central and initial exposed to risk), exact calculation of the central exposed to risk, census approximations to central exposed to risk (trapezium approximation).

11) Graduation : describe the process of graduation and test for the smoothness of graduated estimates.