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Impact of counterparty risk on the reinsurance market. (English) Zbl 1291.91091

Summary: We investigate the impact of counterparty risk (from the insurer’s viewpoint) on contract design in the reinsurance market. We study a multiplicative default risk model with partial recovery and where the probability of the reinsurer’s default depends on the loss incurred by the insurer. The reinsurer (reinsurance seller) is assumed to be risk-neutral, while the insurer (reinsurance buyer) is risk-averse and uses either expected utility or a conditional tail expectation risk criterion. We show that generally the reinsurance buyer wishes to overinsure above a deductible level, and that many of the standard comparative statics cease to hold. We also derive the properties of stop-loss insurance in our model and consider the possibility of divergent beliefs about the default probability. Classical results are recovered when default risk is loss-independent or there is zero recovery rate. Results are illustrated with numerical examples.

MSC:

91B30 Risk theory, insurance (MSC2010)
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