We consider a risk model in which deficits after ruin are covered by a new type of reinsurance contract that provides capital injections which depend on a chosen level of retention . To allow the insurance company's survival after ruin, the reinsurer would have to inject capital . Assuming that these capital injections are not from the shareholders , but rather obtained through such new reinsurance agreements, the problem here is to determine adequate reinsurance premiums. It seems fair to base the net reinsurance premium on the discounted expected value of any future capital injections. Inspired by the results of Huzak et al. (2004) and Ben Salah (2014) on successive ruin events, we show that an explicit formula for this reinsurance premium exists in a setting where aggregate claims are modeled by a subordinator and a Brownian perturbation. This result is illustrated explicitly for two specific risk models and  some numerical examples.
We consider a risk model where deficits after ruin are covered by a new type of reinsurance contract that provides capital injections . To allow the insurance company's survival after ruin, the reinsurer injects capital only at ruin times caused by jumps larger than a chosen retention level. Otherwise capital must be raised from the shareholders for small deficits. The problem here is to determine adequate reinsurance premiums. It seems fair to base the net reinsurance premium on the discounted expected value of any future capital injections. Inspired by the results of Huzak et al. (2004) and Ben Salah (2014) on successive ruin events, we show that an explicit formula for these reinsurance premiums exists in a setting where aggregate claims are modeled by a subordinator and a Brownian perturbation. Here ruin events are due either to Brownian oscillations or jumps and reinsurance capital injections only apply in the latter case. The results are illustrated explicitly for two specific risk models and in some numerical examples.
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Here ruin events are due either to Brownian oscillations or jumps and reinsurance capital injections only apply in the latter case. The results are
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