Why State Definitions Matter
A disability income model is only as meaningful as its state definitions. The label “disabled” does not have one universal contractual meaning: a policy may test whether the insured can perform the duties of their own occupation, whether they can perform any suitable occupation, or whether they satisfy a specific partial-disability provision. Those terms determine how a person’s history is represented in the model.
For a basic disability income model, the life is classified as active, disabled, or dead at each time. This classification describes the insured’s status under a specified set of policy rules. It does not, by itself, determine whether a benefit is currently payable. For example, a person can meet the policy’s disability definition while still serving an elimination period.
For a policy in force, a useful baseline convention is:
- Active: the insured is alive and does not meet the policy’s defined disability test at time \(t\).
- Disabled: the insured is alive and meets that disability test at time \(t\), whether or not a benefit is yet payable.
- Dead: the insured has died. For a model of the covered life, death takes precedence over any disability condition that existed immediately before death.
The model’s disability test must be stated precisely. It may include medical evidence, occupational duties, earnings loss, a specified degree of incapacity, or other contractual conditions. A diagnosis alone does not establish the disabled state unless the policy’s definition makes that diagnosis sufficient.
State Membership Is Not the Same as Benefit Eligibility
An elimination period, also called a waiting period, commonly requires a qualifying disability to continue for a specified duration before benefits begin. That payment condition does not automatically change the date disability began. In a model where state 1 means “meets the disability definition,” the insured enters state 1 when the qualifying condition begins, not when the waiting period ends.
Some policy wording makes a completed period of disability part of the definition of a payable claim. The modeler must then specify whether state 1 represents the underlying disability condition or the status of satisfying the complete claim test. If the purpose is to value benefits, it may be necessary to track elapsed disability duration or claim eligibility in addition to the three states. One state label cannot encode every payment condition.
Worked Example: Disability Begins Before the Elimination Period Ends
A hypothetical policy is in force from time \(t=0\). The insured is active until day 40, when a medically supported condition prevents the insured from performing the duties required by the policy’s own-occupation definition. The condition continues until recovery on day 130. The policy has a 60-day elimination period, measured from the start of continuous qualifying disability. Determine the state history and the benefit-eligible period. For this classification exercise, no interest rate, mortality law, or probability distribution is assumed; the dates and events are given.
Step 1: Identify the state test. The insured meets the stated disability definition from day 40 until recovery on day 130. Thus the state changes from active to disabled on day 40.
Step 2: Apply the elimination period to benefit eligibility. Sixty days after day 40 is day 100. Subject to the policy’s exact day-count and payment-date provisions, benefits can begin on day 100 because the qualifying disability has continued for 60 days.
Step 3: State the result. The state history is active before day 40, disabled from day 40 until recovery on day 130, and active again after recovery, assuming the insured remains alive and the policy remains in force. The potential benefit period is day 100 to day 130, a duration of \(130-100=30\) days.
Check. The insured is disabled for \(130-40=90\) days. The first 60 days satisfy the elimination period, leaving \(90-60=30\) days after the waiting period and before recovery. A common mistake is to put state entry on day 100; that wrongly treats the waiting period as part of the disability definition.
Occupation Tests and Changing Definitions
A policy can use one disability test for an initial period and another afterward. For example, it may first ask whether the insured can perform the material duties of their own occupation, then later ask whether the insured can perform the duties of any occupation for which they are reasonably suited. In that case, state membership is determined by the test applicable at that time. The insured’s medical condition can remain unchanged while the state classification changes because the contractual test changes.
“Active” in this model means “not meeting the applicable disability definition while alive.” It does not necessarily mean working, earning the same income as before, or being free of any medical condition. Likewise, inability to return to one’s former job does not automatically mean the insured remains disabled if the current policy test is an any-occupation test and the insured can perform suitable work.
Worked Example: A Change From Own-Occupation to Any-Occupation
A hypothetical policy defines total disability using an own-occupation test for the first 12 months of disability. After 12 months, it uses an any-occupation test. At time \(t=0\), an insured can no longer perform the material duties of their specialized occupation, but can perform suitable sedentary work. The insured’s abilities remain unchanged through month 15. Assume the policy is in force and no separate partial-disability provision applies. No interest rate, mortality law, or probability distribution is assumed.
Step 1: Apply the initial test. From month 0 up to month 12, the own-occupation test applies. The insured cannot perform the material duties of their own occupation, so the insured is disabled during this period.
Step 2: Apply the later test. At month 12, the any-occupation test applies. The insured can perform suitable sedentary work, so the insured does not meet that test and is classified as active from month 12 onward, subject to the policy’s exact boundary wording.
Step 3: Give the state history. The insured is in state 1 for the first 12 months and state 0 from month 12 through month 15. The medical condition did not improve; the applicable contractual definition changed.
Check. This classification follows the stated tests, not the insured’s job title or whether the insured has actually found work. A common mistake is to keep the insured disabled after month 12 solely because the insured cannot return to the former occupation, ignoring the change to the any-occupation test.
Partial Disability, Recovery, and Recurrence
Some policies provide benefits for partial or residual disability. The contract might require that the insured be unable to perform one or more material duties, have a specified earnings loss, or meet both conditions. When the three-state model is intended to represent the policy-defined disability status, a person who satisfies that partial-disability definition belongs in state 1 even if they can still work part-time or perform some duties.
A recovery occurs when the insured no longer meets the applicable disability definition. A later return to disability is a new change in state status. Whether a later episode is treated as a recurrence of the same claim, is subject to a new elimination period, or has a different benefit limit depends on additional policy wording. Those claim rules must not be inferred merely from the three state labels.
Worked Example: Partial Disability, Recovery, and a Later Episode
A hypothetical policy defines partial disability as a medically supported inability to perform at least one material duty together with an earnings loss of at least 20% compared with the insured’s pre-disability earnings. At month 6, the insured cannot perform a material duty and has a 30% earnings loss. At month 10, the insured can perform all material duties and has a 10% earnings loss. At month 14, a new deterioration prevents performance of a material duty and produces a 25% earnings loss. The insured dies at month 18. Assume the policy remains in force until death. No interest rate, mortality law, or probability distribution is assumed; the sequence is deterministic.
Step 1: Classify month 6 onward. Both partial-disability conditions are met: the insured cannot perform a material duty and the 30% earnings loss exceeds the 20% threshold. The insured enters state 1 at month 6.
Step 2: Classify the improvement at month 10. The insured can perform all material duties, and the 10% earnings loss is below the contractual threshold. The insured no longer meets the stated disability definition, so the state returns to 0 at month 10.
Step 3: Classify the later deterioration. At month 14, the insured again cannot perform a material duty and has a 25% earnings loss. Both conditions are met, so the insured enters state 1 again.
Step 4: Apply the death convention. At month 18, the insured enters state 2. The state history is disabled from month 6 to month 10, active from month 10 to month 14, disabled from month 14 to month 18, and dead from month 18 onward in this covered-life model.
Check. The first and second disability periods are separated by a period that fails both the partial-disability test as stated and the material-duty condition. Whether the later episode is a claim recurrence is a separate contractual question. A common mistake is to classify any earnings loss as disability, even when the policy’s required conditions are not met.
From Contract Wording to a State History
A consistent classification can be made by applying a fixed order of questions at each time. First determine whether the insured is alive and covered. If dead, assign the dead state. If alive, apply the disability definition that is in force at that time, including any change in occupation test or partial-disability criteria. If the insured does not meet that definition, assign the active state. Then assess waiting periods, benefit limits, and claim procedures separately when determining payment.
Decide whether the states represent the insured’s contractual disability status, claim eligibility, or another specified status. State the choice before classifying events.
Record the relevant occupation standard, medical or functional requirements, earnings threshold, and any time-dependent change in wording.
Apply the test to the insured’s facts over time. Use state 1 when the test is met and state 0 when it is not, provided the insured is alive and covered.
Check elimination periods, claim requirements, maximum benefit periods, and payment dates without treating them automatically as state changes.
The logic behind the basic three-state classification is a partition. At any time when the insured is covered, either the insured is dead or alive. If alive, the insured either meets the chosen disability test or does not. These alternatives are mutually exclusive and exhaustive when the test is fully specified and death takes precedence. If \(I_j(t)\) is 1 when the insured is in state \(j\) at time \(t\), and 0 otherwise, then:
This identity is useful when recording a state history: assigning two states at once or leaving a covered time unclassified indicates that the definitions or the facts have not been handled consistently. If the state is treated as random, the same partition implies \(P(X_t=0)+P(X_t=1)+P(X_t=2)=1\). This is a consequence of exhaustive, mutually exclusive states, not a transition model.
Common Modeling Traps
- Starting disability at the first benefit payment. The elimination period usually delays payment, not the onset of the underlying disability state. Confirm which status the model is intended to represent.
- Using a medical label instead of the policy test. A diagnosis does not necessarily satisfy an occupational or functional definition.
- Assuming active means employed and healthy. Active means alive and not meeting the applicable disability test in the chosen model.
- Ignoring a change in the occupation standard. Reapply the test that applies at each time; the state can change even when the insured’s health does not.
- Equating claim approval with state membership. Unless the model explicitly concerns administrative claim status, late notice or delayed approval does not by itself determine when the underlying disability condition began.
- Forcing every policy into three states. If benefits distinguish total from partial disability, or distinguish claim eligibility from disability status, additional states or supplementary variables may be needed for the model’s purpose.
Check Your Understanding
For each hypothetical case, classify the state history and distinguish disability status from benefit eligibility where needed.
- A policy uses the state definition “meets the total-disability test.” The insured is active through day 20, meets that test from day 20 through day 90, and then recovers. The elimination period is 45 days from onset. Give the state intervals and the potential benefit duration. (Answer: Active before day 20; disabled from day 20 to day 90; active after day 90; potential benefits begin on day 65 and continue for 25 days, subject to payment terms.)
- A policy uses an own-occupation test for 12 months and then an any-occupation test. The insured cannot perform their own occupation but can perform suitable work throughout. State the classification during each test period. (Answer: Disabled during the first 12 months under the own-occupation test; active afterward under the any-occupation test, assuming no other disability provision applies.)
- A partial-disability definition requires a material-duty limitation and an earnings loss of at least 15%. An insured meets the duty condition and has an 18% earnings loss, which later falls to 12% while the insured can perform all material duties. Classify both periods. (Answer: Disabled during the first period; active in the later period.)
- An insured satisfies the policy’s disability test from time \(t=5\) to \(t=25\), but the policy requires 30 continuous days of disability before benefits can begin. Under a model where state 1 means meeting the disability test, determine the state and whether a benefit becomes payable. (Answer: Disabled from \(t=5\) to \(t=25\), then active after recovery; no benefit becomes payable because the 20-day disability period is shorter than the 30-day elimination period.)
- An insured meets the policy’s disability definition immediately before death at month 9. The insured dies at month 9, and the covered-life model assigns death priority from that time onward. State the classification at and after month 9. (Answer: Disabled immediately before month 9; dead from month 9 onward.)