IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Maximum likelihood estimators for transition intensities
In a model with states Active, Withdrawn and Dead, a life who is observed Active for 3 years and then withdraws contributes what to the likelihood under constant intensities mu_AW and mu_AD?
The contribution is exp(-3(mu_AW + mu_AD)) times mu_AW: survival in the Active state for three years against both exits, then the density of the observed withdrawal.
- Aexp(-3(mu_AW + mu_AD)) mu_AWCorrect
- Bexp(-3 mu_AW) mu_AW
- Cexp(-3(mu_AW + mu_AD)) mu_AD
- Dexp(-3 mu_AD) mu_AW
- 3 mu_AW mu_AD
Explanation
The life stays in Active for 3 years with probability exp(-3(mu_AW+mu_AD)), then moves to Withdrawn with intensity mu_AW. Leaving out mu_AD from the exponent ignores that death was also a possible exit during the stay.
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