Excess of Loss - An insurance where an insurer's liability to pay for an insured loss, only applies once the loss exceeds a certain amount and then only for liability in excess of that amount.

Excess of Loss policies are usually arranged for risks, which may bring about a significant loss, running perhaps into millions of Pounds. 

An insurer may perhaps be willing to underwrite for a specific amount, at an acceptable level, thereby limiting their liability for the risk.