Derive and apply Kolmogorov's forward equations for continuous time Markov multiple state models.
Free SOA Exam ALTAM (Advanced Long-Term Actuarial Mathematics) lesson in Survival Models for Contingent Cash Flows. 41 min read, ~6,198 words.
A continuous-time Markov multi-state model is defined by transition intensities, the instantaneous rate of moving from state to state. The forward equation tracks how changes as inflow to state minus outflow from; derive it via Chapman-Kolmogorov split plus a first-order intensity expansion. General form:. Boundary values:, for, with row sum...
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