This module aims to provide students with a comprehensive understanding of mathematical and statistical modelling techniques relevant to actuarial work, with a specific focus on risk modelling and survival analysis. The module covers two main topics: random variables and distributions for risk modelling, and survival models. Students will gain theoretical knowledge and practical skills essential for analyzing insurance contracts, estimating lifetime distributions, and forecasting mortality rates.
A. Understand statistical distributions suitable for modelling the variables and risks that arise within insurance contracts. B. Explain the concepts of survival models, including lifetime distributions, survival functions, and hazard rates. C. Apply estimation procedures for lifetime distributions, such as Kaplan-Meier and Nelson-Aalen estimators in the presence of censoring. D. Understand models for proportional hazards and the Cox proportional hazards model for estimating the impact of covariates on hazard rates. E. Perform mortality projection using different models, and assess the main sources of error in mortality forecasts. F. Derive maximum likelihood estimators for transition intensities in Markov models and understand transition intensities dependent on age.
This module will be delivered by a combination of formal lectures and tutorial sessions.