13_AS_5B_lec_annotated

For states i 2 and 3 a life can go directly either to

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Unformatted text preview: σ , ν , ρ) has an asymptotic multivariate Normal distribution (µ, σ , ν , ρ) are asymptotically independent Similar calculations as the simple 2 state model provides asymptotic distribution µ E [V ] σ ∼ Normal σ, σ E [V ] ν E [W ] ρ ∼ Normal ρ, ρ E [W ] µ ∼ Normal µ, ν ∼ Normal ν, 51/60 Actuarial Statistics – Module 5: Parametric methods: Markov Model General Markov Model For a general Markov model, MLE µij of the transition rates ˜ µij (j = i ): µij µij ∼ Normal µij , ˜ , E [Ti ] where Ti is the total waiting time in state i . 52/60 Actuarial Statistics – Module 5: Parametric methods: Markov Model General Markov Model Example A multiple state model has four states 1,2,3 and 4. For states i = 2 and 3, a life can go directly either to i − 1 or to i + 1. For state i = 1, a life can only go i + 1. For state i = 4, a life can only go to i − 1. The force of transition from state i to state j is equal to λ when i < j , and µ when i > j . A large number of lives are in the system and they all beh...
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This document was uploaded on 04/03/2014.

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