Pricing Catastrophe Reinsurance with Reinstatement Provisions Using a Catastrophe Model

In recent years catastrophe reinsurers' use of catastrophe models has been increasing until currently virtually all of the catastrophe reinsurers in the world use a catastrophe model to aid them in their pricing and portfolio management decisions. This paper explicitly models various types of reinstatement provisions, including reinstatements that are limited by the number of occurrences and by the aggregate losses; and reinstatement premiums based on the size of loss and by the time elapsed to the first occurrence. The paper also investigates the effects on the fair premium of a catastrophe treaty when various reinstatement provisions are considered.