13_AS_5B_lec_annotated

# I write down the likelihood function stating any

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Unformatted text preview: h census data often available with number in each state recorded at ﬁxed dates (e.g. 31 December) estimate waiting times by making some simplifying assumptions, eg assuming transitions occur on average half way through the interval 57/60 Actuarial Statistics – Module 5: Parametric methods: Markov Model General Markov Model Exercise A multiple state model has three states. From state 1, 1 lives can only jump to state 2 with transition force σ1 . From state 1 2, they can only jump to state 3 with transition force σ2 and from 1 state 3, they can only jump to state 1 with transition force σ3 . All transition forces are constant. Lives can also enter or exit out of the system at any time. Entry and exit times are deterministic. The system is inspected regularly and Pi (t ) denotes the observed number of lives in state i at time t (t = 0, 1,2, · · · , T). ni denotes the observed number of transitions out of state i over the time period [0, T] (not including the exits). (i) Write down the likelihood function stating a...
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## This document was uploaded on 04/03/2014.

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