We consider the problem of indifference pricing of reinsurance contracts that contain a reinstatement clause. We define the indifference price relative to both a monetary utility function and a risk measure, to take into account both the risk reduction and the relief of capital immobilization provided by reinsurance. We characterize the indifference price as the unique solution to a fixed point equation and we bound the price by two easily computable values, if one has access to losses simulations. We illustrate our results on a European catastrophe insurance portfolio, and we conduct a simulation study for comparison and reproducibility purposes, where we include the case of dependence between claim arrivals, using Hawkes processes.

我们考虑了包含恢复条款的再保险合同的无差别定价问题。我们定义相对于货币效用函数和风险度量的无差异价格，要考虑到再保险提供的风险降低和资本固定化的缓解。我们将无差异价格定性为定点方程的唯一解，如果可以访问损失模拟，则将价格限制在两个易​​于计算的值上。我们用欧洲巨灾保险产品组合说明了我们的结果，并进行了比较和可复制性目的的模拟研究，其中包括使用Hawkes流程得出索赔到达之间的依存关系的情况。