Calculate state-dependent probabilities for continuous time Markov models.
Free SOA Exam ALTAM (Advanced Long-Term Actuarial Mathematics) lesson in Survival Models for Contingent Cash Flows. 22 min read, ~3,228 words.
Notation: is the probability a life in state at age is in state at age. The overline requires staying in throughout. Boundary/identity: with zero off-diagonal, and at every; absorbing states accumulate the departing mass. Sojourn formula:, summing over every exit from. First-transition integral: for simple no-return path structures one integral...
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- Example 2
- Example 3
- Example 4
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