Health Insurance

A long-term disability income policy is described with given incidence and termination rates, and you must compute the gross premium.

Use a multi-state model with states active, disabled (sometimes by duration), and dead. Compute APV of disability benefits using the active-to-disabled and disabled-to-active transition intensities. Add expenses and profit, then solve the equivalence equation for premium. For LTC, model duration in claim with termination rates depending on cause and duration.

APV(benefit) involves active-to-disabled transition and continuance probabilities while disabled.

A block of LTC or DI policies in different states (active, disabled) is given and you must compute active life reserves and disabled life reserves.

Active life reserve (ALR): APV of future benefits net of future premiums for an active life, valued under multi-state mortality and morbidity. Disabled life reserve (DLR): APV of remaining benefits for an in-claim life, using duration-since-disablement-dependent termination rates. Disabled life reserves are usually computed by continuance tables or by integration of survival in the disabled state.

ALR for active lives; DLR for disabled lives; both use multi-state probabilities.

A health insurance block has rising claim costs due to medical trend and shows signs of antiselection at renewal.

Decompose claim cost growth into utilization trend, unit cost trend, leveraging, mix, and aging. Trend losses forward to the rating period. For antiselection, model deteriorating average risk as healthy lives lapse: rate increases drive a worsening risk pool, requiring further increases — the "death spiral". Discuss community vs experience rating as mitigation.

Total trend = utilization × unit cost × leveraging × mix; antiselection = adverse lapse pattern.