In proportional reinsurance, the insurer (cedent) and the reinsurer agree to share both premiums and losses on a specified class of business in a pre-agreed proportion. This is one of the most common forms of reinsurance.

Let's denote the retention proportion for the insurer as , where . Consequently, the proportion ceded to the reinsurer is .

For any single claim with amount , the claim is divided between the insurer and the reinsurer as follows:

• The insurer's liability (retained loss) is .
• The reinsurer's liability is .

It is clear that the sum of the payments from both parties equals the total claim amount: .

Expected Payments and Variance

The expected payment for each party is also proportional to the total expected claim amount.

Insurer (Cedent)

The expected payment per claim for the insurer is:

The variance of the insurer's payment is:

By ceding a portion of the risk, the insurer reduces the variance of its claims experience, leading to more stable results.

Reinsurer

Similarly, the expected payment per claim for the reinsurer is:

And the variance of the reinsurer's payment is:

Premiums

Just as losses are shared, the premium for the policy is also shared in the same proportion. If the total premium for a policy is , then:

• The insurer retains a premium of .
• The reinsurer receives a premium of .

This arrangement ensures that both the potential for profit (from premiums) and the risk of loss are distributed between the two parties.