multiple-state (Markov) models
/ Markov = MAR-kof /
Some insured situations are not just 'alive or dead' but a journey through several conditions that you can move between, sometimes back and forth. Think of long-term-care or disability insurance: a person can be healthy, become disabled, recover back to healthy, or die at any point. A multiple-state model draws this as a set of boxes (states) connected by arrows (possible transitions), and attaches a rate to each arrow. It is the natural generalisation of survival models once 'leaving' is replaced by 'moving around'.
The 'Markov' part is a simplifying assumption: where you go next depends only on the state you are in now, not on the full history of how you got there. So a currently-disabled life has the same chance of recovering regardless of how long ago they first fell ill (in the simplest version). Each arrow carries a transition intensity, the multi-state cousin of the force of mortality, and the model lets you compute the probability of being in any given state at any future time. Ordinary survival is the two-state special case (alive then dead), and multiple-decrement models are the special case where every arrow leads to an absorbing exit you can never return from.
Multiple-state models are the modern backbone of disability income, long-term care, critical illness, and continuing-care valuations, and they appear in the international actuarial education syllabus as the unifying framework for life contingencies. Their honesty depends on the transition rates being well estimated and on the Markov assumption being reasonable; when recovery really does depend on duration of sickness, a strict Markov model can mislead, and a richer (semi-Markov) model is needed.
A disability model with states Healthy, Disabled, Dead has arrows for falling sick, recovering, and dying; the transition intensity from Healthy to Disabled plays the same role that the force of mortality plays in a plain life model.
Boxes for states, arrows for transitions, a rate on each arrow — survival models generalised.
The Markov assumption (the future depends only on the current state) is a convenience, not a law of nature. If recovery odds really depend on how long someone has been sick, a strict Markov model understates that, and a semi-Markov approach is needed.