Final answer:
The reinsurance agreement between Liability Insurance Company (LIC) and the reinsurer, where they share both the premiums and losses based on a fixed percentage, is best described as proportional reinsurance.
Step-by-step explanation:
The question at hand involves a situation where the Liability Insurance Company (LIC) was approached by a regional airline to see if LIC would write the airline's liability coverage. LIC agreed to write the coverage and made an arrangement with a reinsurer where LIC retains 25 percent of the premium and covers 25 percent of the losses, with the reinsurer taking on the remaining 75 percent of the premium and losses. This type of arrangement where both the premiums and losses are shared proportionally between the insurer and the reinsurer is known as proportional reinsurance.
In proportional reinsurance, also known as treaty reinsurance, the primary insurer and the reinsurer agree to share the premiums and losses based on a fixed percentage. This contrasts with excess reinsurance, where the reinsurer is responsible for losses that exceed a certain amount and retrocession, which is when a reinsurer obtains reinsurance for itself. Co-insurance, on the other hand, typically refers to the sharing of risk between the insurer and the policyholder, not between an insurer and a reinsurer.