Minimising expected discounted capital injections by reinsurance in a classical risk model

Abstract

In this paper we consider a classical continuous time risk model, where the claims are reinsured by some reinsurance with retention level , where means ‘no reinsurance’ and b=0 means ‘full reinsurance’. The insurer can change the retention level continuously. To prevent negative surplus the insurer has to inject additional capital. The problem is to minimise the expected discounted cost over all admissible reinsurance strategies. We show that an optimal reinsurance strategy exists. For some special cases we will be able to give the optimal strategy explicitly. In other cases the method will be illustrated only numerically.