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Chapter 25 Finite Risk Contracts Insurers (and reinsurers) also offer multiple year loss sensitive plans that commonly are called finite risk...

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Using the finite risk contract found in the attachment, how much would the policy holder get back at the end of three years if loss payments at year-end were:
a. $3 million in year 1; $3 million in year 2; and $3 million in year 3?
b. $8 million in year 1; $1 million in year 2; and $1 million in year 3?

Chapter 25 Finite Risk Contracts Insurers (and reinsurers) also offer multiple year loss sensitive plans that commonly are called finite risk insurance or financial insurance. The term finite risk is used to indicate that there is relatively little risk transferred to the insurer. In other words, the insured firm usually pays most of the losses. The contract period for finite risk contracts often is three to five years. The insured firm pays premiums each year to the insurer who places the premiums in a fund (after taking out a fee). The fund accumulates interest at an agreed upon rate of return, the losses are paid from the fund. If the fund is insufficient to pay all the losses in a given year, then the insurer will pay losses up to a stated limit. However, the policyholder’s future premium payments are used to reimburse the insurer. Any surplus remaining in the fund at the end of the policy period is returned to the insured firm. Together, these features imply that the policyholder pays most losses, but that the payments are smoothed over time. Thus, finite risk plans provide protection against the timing of loss payments but offer limited protection against unexpected loss payments over the course of the policy period. An example will help illustrate the essential aspects of finite risk contracts. Suppose that a three-year contract is signed that (1) requires the insured firm to pay premiums of $4 million a year, (2) credits interest at 6.0 percent annually on the year’s beginning balance, (3) provides the insurer with a fee equal to 10 percent of each premium, and (4) has an aggregate limit of $20 million for the three-years. The following table illustrates the cash flows that would occur if paid losses in the tree-years equal $2 million, $4 million, and $5 million respectively. We assume for simplicity that these loss amounts are paid at the end of each year. In the first year, the policyholder pays the premium of $4 million, the insurer takes its fee, and the interest is earned on the balance. Since claim payments at the end of the first year equal $2 million, all claims are paid from the policyholder’s fund. The ending balance in the fund after the first year equals $1,816,000. The premium payment in the second year increases the size of the fund, so that even though claim payments equal $4 million at the end of year 2, the policyholder’s fund again is sufficient to pay all claims. The same scenario occurs in year 3; the policyholder’s fund has enough money to pay all claims, leaving a surplus of $661,418. In this example, the $661,418 remaining in the fund at the end of the policy period would be returned to the policyholder. Alternatively, if another finite risk plan were established for the subsequent three-year period, the surplus at the end of the first three-year period could be used to reduce the premiums for the second three-year-period. Year 1 Year 2 Year 3 At the Beginning of the year Balance from previous year $ 0 $ 1,816 $ 1,741 Premium 4,00 0 4,00 0 4,00 0 Insurer’s fee -40 0 -40 0 -40 0 Beginning balance 3,60 0 5,41 6 5,34 1 At End of Year
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Claim payments -2,00 0 -4,00 0 -5,000 Interest on beginning balance 21 6 32 5 32 0 Ending balance $ 1,816 $ 1,741 $ 661 *Cash Flows (in thousands) from a three-year finite risk contract (premium=$4 million; interest = 6% of beginning balance; $20 million aggregated limit). Notice that in the example, the insured firm has essentially paid all losses because claims were always below the amount in the fund. If losses were to exceed the amount in the fund, then the insurer would have to pay the losses up to the limit of $20 million. Thus, finite risk insurance is similar to a multiyear policy with a high deductible. The following table illustrates the same policy as before, but with higher overall loss payments. In particular, claim payments equal $1 million, $12 million, and $1 million respectively, at the end of years one through three. The large claim payment at the end of the second year depletes the policyholder’s fund, so the insurer makes up the shortfall by paying $5,199,000. As a consequence, the policyholder’s fund has a deficit after two years. In this example, the deficit is larger than the premium payment in the third and final year, which implies that the insurer will pay some of the insured’s losses (up to $20 million aggregate limit). Finite risk contracts also can have provisions that make the policyholder pay a large percentage (e.g. 80 or 90 percent) of any deficit in the fund at the end of the policy period. The payment of the deficit usually can be paid in installments, thus allowing the policyholder to spread the costs over time. For example, in the previous example, a $2,695 million deficit existed at the end of the policy period. The contract could require that the policyholder pay 80 percent of this amount in equal installments over the subsequent three-years. This $898,327 payment (0.80 x $2,695,000 / 3) also could be added to the premium for another finite risk contract over the subsequent three-year time period. This example illustrates that while the policyholder bears most of the risk of unexpected losses with finite risk plans, these plans allow firms to smooth their payments for losses over time. Year 1 Year 2 Year 3 At beginning of the year: Balance from previous year $ 0 $ 2,816 - $5,199 Premium 4,00 0 4,00 0 4,00 0 Insurer’s fee -40 0 -40 0 -40 0 Beginning balance 3,60 0 6,41 6 -1,59 9 At end of year: Claim payments -1,00 0 -12,00 0 -1,00 0
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