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 threeyear 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 threeyears. 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 threeyear 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