This paper studies a Pareto-optimal reinsurance contract in the presence of negative statistical dependence between the insurance claim and the random recovery rate. In the context of symmetric information model and asymmetric information model, we investigate properties of the Pareto-optimal indemnity schedules. For risk neutral reinsurer with proportional cost and associated expense, we present possible forms of the Pareto-optimal indemnity schedule as well.Risks 2018, 6, 114 2 of 16 and uninsurable risks, Dana and Scarsini (2007) investigated qualitative properties of Pareto-optimal insurance contracts.Besides the additive one, the multiplicative background risk is quite common in the insurance practice. The counter-party risk in a reinsurance contract, which means the little chance that the reinsurer fails to pay the entire promised benefit to the insurer, is the default risk of the reinsurer. Readers may refer to Franke et al. (2006) for a comprehensive study on the multiplicative background risk. In the existing literature, researchers studied various characterizations of the counter-party risk together with its impact on the design of optimal reinsurance contract. For example, Tapiero et al. (1986) employed the perceived probability of ruin to characterize the probability of the insurer being affected by the reinsurer's default risk, and Schlesinger and Schulenburg (1987) considered a three-state model in which a loss that can not be indemnified occurs with a nonnegative probability, and discussed how insurance purchases are affected by the insurer's level of risk aversion. In the four-state model of Doherty and Schlesinger (1990), both the reinsurer and the insurer know the default probability, and the partial insurance is proved to be optimal when the reinsurer has a positive probability of total default. Later, such a result was extended to partial default by Mahul and Wright (2007). On the other hand, Cummins and Mahul (2003) derived the optimal insurance in the context that the reinsurer has a positive probability of total default and the reinsurer and insurer have divergent beliefs about this probability. Recently, Bernard and Ludkovski (2012) considered loss-dependent probability of default and partial recovery in the event of contract non-performance, and studied the Pareto-optimal reinsurance contracts with counter-party risk for risk neutral reinsurer and risk averse insurer. Thus, Bernard and Ludkovski (2012) extended the model of Dana and Scarsini (2007) to the case of multiplicative but not additive background risk.Usually, the background risk has significant impact on the Pareto-optimal reinsurance contract, and as is pointed out in Franke et al. (2006) and Bernard and Ludkovski (2012), the presence of multiplicative background risk can be more complex than the additive risk. On the other hand, in the presence of multiplicative background risk, Bernard and Ludkovski (2012) only dealt with binary recovery rate and risk neutral insurer with linear cost. In this study, we consider the reinsuranc...