## Minimising expected discounted capital injections by reinsurance in a classical risk model.(English)Zbl 1277.60145

Summary: In this paper we consider a classical continuous-time risk model, where the claims are reinsured by some reinsurance with retention level $$b\in[0,\tilde b]$$, where $$b=\tilde b$$ 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.

### MSC:

 60K10 Applications of renewal theory (reliability, demand theory, etc.) 62P05 Applications of statistics to actuarial sciences and financial mathematics 91B30 Risk theory, insurance (MSC2010) 93E20 Optimal stochastic control
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### References:

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