Which of the following scenarios would typically be eligible for excess of loss reinsurance?

Excess of loss reinsurance is a form of reinsurance that is designed to protect insurers against high levels of loss that can arise from unpredictable and catastrophic events. This type of reinsurance kicks in when the losses exceed a predetermined threshold, known as the retention limit, thereby providing the insurer with coverage for large, unexpected claims.

In the context of the scenarios provided, unpredictable catastrophic events leading to heavy losses perfectly align with the purpose of excess of loss reinsurance. Such events are characterized by their potential to result in significant financial impact beyond the insurer's capacity to absorb, making this type of reinsurance essential for managing the risk associated with large-scale disasters.

The other options, though they represent various types of claims or costs an insurer might face, do not typically qualify for excess of loss reinsurance. Small claims incurred frequently may be better suited for different forms of insurance arrangements, such as quota share agreements. Routine operational costs of insurers are part of regular business expenses and do not relate to loss reinsurance. Minor property damage claims would generally fall below the threshold that triggers excess of loss coverage since they usually do not lead to the heavy losses envisioned in this type of reinsurance arrangement.