ETC5343 Financial mathematics under uncertainty

When you finish this unit, you should be able to:

1. 1

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

2. 2

   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

3. 3

   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

4. 4

   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

5. 5

   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

6. 6

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

7. 7

   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

8. 8

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

9. 9

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