Optimal Premium Plans for Reinsurance with Reinstatements

Abstract

The present paper is concerned with optimal premium plans for a reinsurance contract with reinstatements. In the reinsurance contract considered here, constant reinstatement premiums are due when the reinsurer’s loss exceeds certain bounds. For this reinsurance contract we examine the existence of a premium plan which minimizes the expected squared difference between the loss and the total premium income of the reinsurer. We show that an optimal premium plan exists, that it is unique, and that it satisfies the net premium principle.

Indifference pricing of reinsurance with reinstatements using coherent monetary criteria

“…To avoid computing the probability law of the aggregate losses, Hürlimann [17] provides a distribution free approximation to pure premiums of layers with reinstatements, using maximal distributions for certain stochastic orders under moment constraints on the claim arrival process, and on the claim size distribution. The authors of [15] take an optimal contract point of view: the reinsurance contract parameters are chosen in order to minimize the expected distance between the loss and the premium income. In a time dynamic setting, [25] and [26] study the ruin probability of a cedent having reinsurance with reinstatements, first with a pure premium assumption and then under standard deviation and PH-transform principles.…”

Excess of Loss Reinsurance with Reinstatements Revisited

“…The main papers on the subject have been Simon(1972) and Sundt(1991). More recent discussions include Walhin(2001Walhin( /2002, Paris(2000/2001a/b), Mata(2000), Hess and Schmidt(2004).…”