Delta Insurance is a property insurer that entered into a surplus-share reinsurance treaty with Eversafe Re. Delta has a retention limit of $200,000 on any single building, and up to nine lines of insurance may be ceded to Eversafe Re. A building valued at $1,600,000 is insured with Delta. Shortly after the policy was issued, a severe windstorm caused an $800,000 loss to the building.
a. How much of the loss will Delta pay?
b. How much of the loss will Eversafe Re pay?

D entered in surplus share reinsurance treaty with E. D has a retention limit of $200,000 for a single building and up to nine lines of building can be ceded to E.

The value of the building is $1,600,000 and there is a loss of $800,000. Compute the loss that delta will pay in the following manner: Compute the underwriting capacity of 0 as follows:

Underwriting capacity = $200,000 + $200,000 x 9

= $200, 000 + $1,800, 000

= $2, 000,000

Therefore, the underwriting capacity of D is $2, 000,000

The policy issued is for $1.600.000. Compute the fraction of D and E as follows:

D = 200000 / 1600000

D = 1/8th

E = 1400000 / 1600000

E = 7/8th

Therefore: the fraction of D is 1/8th and fraction of E is 7/8th

Compute the loss to be borne by D as follows:

Loss borne by D = Total loss x Fraction of D

Loss borne by D = 800,000 x 1/8

Loss borne by D = 100000

Therefore, the loss to be borne by D is 100000

Part b.

Compute the amount that E would pay in the similar manner.

E would share for seven eighth of the loss. Here, the loss is of $800,000.

Loss borne by E = Total loss x Fraction of E

Loss borne by E = 800,000 x 7/8

Loss borne by E = 700,000

Therefore, the loss repay by E is 700000

Part c.

This is a case of surplus share treaty where the re insurer accepts the insurance exceed in the retention limit of ceding company up to the maximum amount.

D has a retention limit of $200,000 for a single building so the total underwriting capacity for the 10 buildings will be 2000000