A short technical primer on the excess-of-loss layer, expected loss, rate on line and the risk load that turns loss cost into premium.
Every excess-of-loss layer can be read as a simple transformation of loss. A layer of limit l excess of retention d pays the part of a loss above d, capped at l. Its expected cost is the area under the loss survival curve between the attachment and the exhaustion point, pure geometry once you have the severity distribution.
From loss cost to premium
The expected loss is only the starting point. Because a layer's outcome is skewed and volatile, the technical premium adds a risk load for that volatility, plus expenses and the cost of capital. Express the result as a rate on line, premium over limit, and its reciprocal gives the payback period.
For the full treatment, see Excess of Loss Mathematics and Reinsurance Pricing Methods.
Power Re perspective
This commentary reflects Power Re’s reading of public market reporting. It is general information, not underwriting, investment or legal advice.
