A Health Stories Model of Long-Term Care Insurance

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In the United States and other nations, long-term care insurance indemnifies the insured for expenses incurred or provides a daily benefit while the insured cannot perform basic activities of daily living, such as dressing, bathing, eating, toileting, or has a severe cognitive impairment, such as Alzheimer's disease. This Demonstration develops a simplified model of long-term care insurance that uses "health stories". A "health story" is simply a description of the health of a person—"healthy," "LTC", or "dead"—measured at discrete time intervals. The LTC-state means that a person is potentially eligible for long-term care insurance payments based on an inability to perform basic activities of daily living or has a severe cognitive impairment. This Demonstration creates a parameterized model of long-term care insurance that calculates, among other values, the size of the break-even actuarial premium for a group of sample insureds given a user-specified contract and other factors such as expected interest rates and insurer expense loads. It also calculates reserves on long term care policies as they age.


You choose from seven groups of parameters: (1) model size, (2) insured age, (3) health-LTC-death transition parameters, (4) insurance contract parameters, (5) miscellaneous parameters, (6) a view parameter to determine the form of the output, and (7) view-specific controls that may have relevance only when a particular view is chosen. Each parameter contains a tooltip that helps explain its function. More information regarding the controls is contained in the Details section of this Demonstration.

Depending on your selection for the view parameter, the Demonstration outputs one of three presentations.

Summary view shows the distribution among the insureds of life span and LTC-years. It also shows the break-even LTC insurance premium as a fraction of annual indemnity.

Story view shows a summary of key contract features and a plot showing, either for each insured or for selected insureds, the cumulative years of being in the LTC state for each year of their life. Blue points along these story lines means the insured is healthy; larger green points mean the insured is in an LTC state and receiving an indemnity; red points mean the insured is not receiving an indemnity.

Reserve view shows up to three loci for each year the policy is in effect: (1) [blue] the prospective reserve—the difference between the present expected value (a) of premiums to be received by the insurer and (b) expenses (loads and indemnities) to be paid by the insurer; (2) [magenta] the expected accumulated premiums—the amount the insurer expects to have collected, a figure that is sometimes used as the basis for computing a reduced indemnity amount in the event the insured lets the policy lapse in midstream; and (3) [dotted gold] the maximum amount the insurer could pay under the policy.


Contributed by: Seth J. Chandler (March 2011)
Inspired by: S. Haberman and E. Patacco
Open content licensed under CC BY-NC-SA



Snapshot 1: summary view with the default control values

Snapshot 2: story view with the default control values

Snapshot 3: reserve view with the default control values

Snapshot 4: reserve view with the default controls but initial load set to 0.4

The model size determines the number of "health stories" created. Low values result in relatively swift outputs; larger values update output asynchronously from movement of the controls.

The insured age parameter determines the age of the insured at the time they purchase the policy. Persons who purchase insurance at a higher age tend to transition more frequently from healthy to LTC, from healthy to dead, and from LTC to dead, and tend to transition less frequently from LTC to healthy.

There are seven health-illness-death transition parameters. The parameters and determine the "force of mortality" as a function of age. The parameters and similarly determine the "force of LTC" as a function of age. The parameters and determine the relationship between age and the likelihood that a person in the LTC state will transition back to health. The parameter adjusts the "as if" mortality of an LTC person, making their mortality rate equal to what it would be at more years than their actual age had they been in the healthy state.

The insurance contract parameters determine both how the flow of premiums vary for each health story, and the "coverage": how the indemnities between insured and insurer likewise vary for each health story. You choose an "inception window" that determines the time in which a spell of LTC must have persisted in order to require the insured to pay an indemnity to the insured for each otherwise covered year. The "waiting period" and "policy term" define this window. You likewise choose a "cumulative LTC window" that conditions the insurer's obligation to pay in a given time period on whether the cumulative amount of time the insured has been in the LTC state falls between a lower and upper bound. The lower bound is generally known as a "deferred period" or "elimination period". The upper bound is often known as a "maximum benefit period". You likewise determine an ultimate "indemnity stopping time", which excuses the insurer from an otherwise existing duty to indemnify if the length of time between policy inception and a given year exceeds the specified value. You set an indemnity inflation rate that specifies the rate at which the expected indemnity payment will increase over time. Finally, you select three parameters relating to the insured's premium obligation. The "waive premium if LTC" control lets you excuse the insured from an otherwise existing duty to pay a premium in a given time period if they are in an LTC state during that time period. Two controls, "begin premium" and "end premium", create a window that bounds the time periods in which the insured must make payments to the insured.

Although, as this Demonstration shows, the "reserves" of the insurer—the difference between the expected present value of indemnities and the expected present value of premiums—is often positive, insureds who release their insurer from further obligation, by for example lapsing their policies, often get nothing back. Although it is seldom exercised, insureds often have the right to purchase "non-forfeiture protection" under which, in exchange for an additional premium, they receive a reduced benefit in the event the policy lapses, often a policy with a maximum amount equal to the amount of premiums paid in prior to the lapse. In addition, in some American states an insured not purchasing non-forfeiture protection is entitled by law to "contingent non-forfeiture" under which, if the insured increases its premium in the middle of the policy by over a scheduled amount, the insured receives a reduced benefit in the event the policy lapses, which is again often a policy with a maximum amount equal to the amount of premiums paid in prior to the lapse.

This Demonstration makes extensive use of the Mathematica compiler to gain speed.

An explanation of some of the theory behind this Demonstration may be found in S. Haberman and E. Pitacco, Actuarial Models for Disability Insurance, Boca Raton, FL: Chapman and Hall/CRC, 1999.

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