Apply the Chapman-Kolmogorov equations to calculate discrete time transition probabilities in the Markov model.
Free SOA Exam ALTAM (Advanced Long-Term Actuarial Mathematics) lesson in Survival Models for Contingent Cash Flows. 10 min read, ~1,544 words.
CK equation:, summing over every state the chain could occupy at the split time. Matrix form: time-homogeneous gives; time-inhomogeneous gives the ordered product, read left to right. Markov property is the engine: conditional on the current state, the future ignores the past, which is what lets you condition on and...
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