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Proportional Reinsurance

In proportional reinsurance, premium and losses are shared in the same proportion; quota share and surplus are the two principal forms.

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Under proportional (pro-rata) reinsurance, the reinsurer shares an agreed proportion \\(c\\) of premiums and losses. The recovery on any loss is simply \\(R(X)=c\,X\\).

Quota share, cede 40% of every riskRetained 60%Ceded 40%Surplus, retained line 3 on a sum insured of 10Retained 3Ceded surplus 7 (70%)
Quota share cedes a fixed percentage; surplus cedes the amount above a retained line.

Quota share

A fixed percentage \\(c\\) of every risk is ceded, so \\(R(X)=c\,X\\). Simple and strongly aligned, but it cedes premium on business the cedant could have retained.

Worked example

Cede \(c=40\%\). On a \(2\text{M}\) loss the reinsurer pays \(0.4\times 2 = 0.8\text{M}\), and receives 40% of the premium less a ceding commission.

Surplus

The cedant sets a retained line \\(R\\) and cedes only the surplus above it. On a policy with sum insured \\(S\\), the ceded proportion is:

Ceded share, surplus
$$c(S)=\max\!\left(0,\;\frac{S-R}{S}\right)$$

Worked example

Retained line \(R=3\), sum insured \(S=10\). Ceded share \(c=(10-3)/10=70\%\). Small risks with \(S\le 3\) are retained in full.

Ceding and profit commission

The reinsurer pays a ceding commission on ceded premium, often with a profit commission \\(PC\\) that returns a share \\(p\\) of the treaty profit:

Profit commission
$$PC = p\,\big[\,\text{Premium} - \text{Losses} - \text{Commission} - \text{Margin}\,\big]^{+}$$
Positive part only; the reinsurer shares favorable experience with the cedant.

Types of ceding commission

  • Flat (fixed) commission, a constant percentage of ceded premium.
  • Sliding-scale commission, it rises or falls with the actual loss ratio, between a minimum and a maximum.
  • Profit (contingent) commission, a share of favorable treaty experience.
  • Overriding commission, an extra allowance on business placed through intermediaries.

The commission as a price lever

In practice the ceding commission is the reinsurer’s main price lever on a proportional treaty, calibrated against the basic loss ratio (BLR), a burning-cost / frequency component and exposure.

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