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

作者：Eisenberg Julia; Schmidli Hanspeter^*

来源：Scandinavian Actuarial Journal, 2011, 2011(3): 155-176.

DOI：10.1080/03461231003690747

• Optimal control
• Stochastic control
• Hamilton-Jacobi-Bellman equation
• Capital injections
• Classical risk model
• Reinsurance

In this paper we consider a classical continuous time risk model, where the claims are reinsured by some reinsurance with retention level b is an element of [0, <(b)overtilde >]; where b = (b) over tilde 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.

• 出版日期2011