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📋 '''Survival model''' is a statistical framework used in insurance to estimate the probability that a life, contract, or exposure will persist — or "survive" — beyond a given point in time. Rooted in [[Definition:Actuarial science | actuarial science]], survival models underpin the construction of [[Definition:Mortality table | mortality tables]], [[Definition:Morbidity table | morbidity tables]], and [[Definition:Lapse rate | lapse rate]] assumptions that drive pricing, [[Definition:Reserving | reserving]], and [[Definition:Valuation | valuation]] across [[Definition:Life insurance | life]], [[Definition:Health insurance | health]], and [[Definition:Annuity | annuity]] products. The core mathematical object is the survival function, S(t), which gives the probability of surviving to at least time t, and its complement — the cumulative distribution function — which captures the probability of the event (death, disability, policy lapse) occurring by time t.

📊 In practice, [[Definition:Actuary | actuaries]] build survival models by fitting parametric distributions (such as Gompertz, Makeham, or Weibull functions) or non-parametric estimators (such as the Kaplan-Meier method) to observed data on policyholder experience. The [[Definition:Hazard rate | hazard rate]], or force of mortality in life insurance terminology, is a closely related quantity that expresses the instantaneous rate of event occurrence at time t, conditional on survival to that point. Cox proportional hazards models allow the incorporation of covariates — age, gender, smoking status, policy duration — so that risk factors can be quantified and segmented. These models feed directly into [[Definition:Premium | premium]] calculations under both traditional [[Definition:Net premium valuation | net premium valuation]] and modern frameworks: [[Definition:IFRS 17 | IFRS 17]] requires insurers globally to use best-estimate assumptions about future cash flows, which are fundamentally built on survival model outputs, while [[Definition:Solvency II | Solvency II]]'s technical provisions demand explicit [[Definition:Best estimate liability (BEL) | best estimate]] projections of policyholder longevity and decrement rates.

🧮 The significance of survival models reaches into nearly every strategic decision an insurer makes regarding long-duration obligations. Misjudging the survival characteristics of an annuitant population, for example, can lead to severe [[Definition:Longevity risk | longevity risk]] — a challenge that has prompted the development of dedicated [[Definition:Longevity swap | longevity swaps]] and [[Definition:Insurance-linked security (ILS) | insurance-linked securities]]. In [[Definition:Health insurance | health insurance]], survival models inform the estimation of claim durations for disability and long-term care products, where the length of benefit payments depends directly on how long a claimant survives in a disabled state. With the growing availability of granular data and advances in [[Definition:Machine learning | machine learning]], insurers are increasingly layering predictive analytics on top of classical survival frameworks, improving segmentation and enabling dynamic [[Definition:Experience study | experience studies]] that update assumptions in near-real time. Whether applied to mortality, [[Definition:Persistency | persistency]], or claims run-off, the survival model remains one of the most essential quantitative tools in the insurance actuary's repertoire.

'''Related concepts:'''
{{Div col|colwidth=20em}}
* [[Definition:Mortality table]]
* [[Definition:Hazard rate]]
* [[Definition:Longevity risk]]
* [[Definition:Actuarial science]]
* [[Definition:Experience study]]
* [[Definition:Decrement table]]
{{Div col end}}

Definition:Survival model - Revision history

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