Handbook

describe and classify stochastic processes including counting processes and understand state and time spaces and mixed processes

define and apply the Markov Chain and Chapman-Kolmogorov equation; understand the stationary distribution, experience rating systems, time homo and inhomo-geneous Markov Chains and application of such as modelling tools

define and apply a Markov process. Understand the poisson process as a counting process derive and solve Kolmogorov equations, understand and solve multiple state models including the HSD model, generalise to models where transition also depends on duration of stay in a state and describe how to model using such models

explain concept of survival models, lifetime models, distribution and density functions for future lifetime, force of mortality, actuarial notation, life expectancy (complete and curtate) and the two-state model

describe estimation procedures for lifetime distributions. Identify censoring by types and problems caused by censoring; understand and apply the Nelson-Aalen and Kaplan-Meier estimation procedures and the Cox proportional hazards model

derive maximum likelihood estimators for transition intensities and functions for constant transition models

estimate transition intensities dependent on age (exact or census); understand the principle of correspondence, calculate central and initial exposures, explain the concept of rate intervals, estimate initial and central mortality rates from census data and death data

describe and carry out graduation of mortality data and understand and apply graduation tests

describe approaches to forecasting mortality rates; discuss some of the more commonly used forecasting approaches including p-splines, time series modelling and APC models.