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🔗 '''Markov chain''' is a mathematical model describing a system that transitions between a set of states, where the probability of moving to the next state depends only on the current state — not on the sequence of states that preceded it. In insurance, actuaries and data scientists use Markov chains to model dynamic processes such as [[Definition:Policyholder | policyholder]] behavior, [[Definition:Claims | claims]] development, [[Definition:Disability insurance | disability]] recovery trajectories, and [[Definition:Credit risk | credit]] migration in [[Definition:Investment portfolio | investment portfolios]]. The "memoryless" property — known formally as the Markov property — makes these models both tractable and surprisingly effective for capturing real-world insurance phenomena that evolve over time.

⚙️ A typical application involves defining a finite set of states — for instance, "active policy," "lapsed," "claim open," "claim settled," and "policy canceled" — and estimating transition probabilities from historical data. Once calibrated, the model can project the expected distribution of a [[Definition:Book of business | book of business]] across those states at future points in time, feeding into [[Definition:Reserve | reserving]], [[Definition:Cash flow | cash flow]] forecasting, and [[Definition:Pricing model | pricing models]]. Multi-state Markov models are especially prevalent in [[Definition:Life insurance | life]] and [[Definition:Health insurance | health insurance]], where an insured individual may move between "healthy," "disabled," "recovered," and "deceased" — each transition carrying distinct financial implications for the [[Definition:Insurance carrier | carrier]]. More advanced variants, such as hidden Markov models, allow actuaries to infer unobservable risk states from claims data patterns.

📐 The practical value of Markov chains lies in their ability to distill complex longitudinal dynamics into a structured framework that supports rigorous decision-making. [[Definition:Actuary | Actuaries]] rely on them when setting [[Definition:Premium | premiums]] for products with state-dependent benefits, such as [[Definition:Long-term care insurance | long-term care insurance]] or [[Definition:Critical illness insurance | critical illness]] covers, where the cost of a policy hinges on how long and how often an insured occupies a benefit-triggering state. As [[Definition:Insurtech | insurtech]] platforms generate richer behavioral and telematics data, the inputs available for calibrating these models have expanded considerably — enabling more granular segmentation and, ultimately, more accurate [[Definition:Risk assessment | risk assessment]].

'''Related concepts'''
{{Div col|colwidth=20em}}
* [[Definition:Actuarial model]]
* [[Definition:Predictive analytics]]
* [[Definition:Reserving]]
* [[Definition:Multi-state model]]
* [[Definition:Stochastic modeling]]
* [[Definition:Life insurance]]
{{Div col end}}

Definition:Markov chain - Revision history

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