We solve a Stackelberg differential game between a buyer and a seller of insurance policies, in which both parties are ambiguous about the insurable loss. Both the buyer and seller maximize their expected wealth, plus a penalty term that reflects ambiguity, over an exogenous random horizon. Under a mean-variance premium principle and a general divergence that measures the players' ambiguity, we obtain the Stackelberg equilibrium semi-explicitly. Our main results are that the optimal variance loading equals zero and that the seller's robust optimal premium rule equals the net premium under the buyer's optimally distorted probability. Both of these important results generalize those we obtained in [Cao, J., Li, D., Young, V. R. & Zou, B. (2022). Stackelberg differential game for insurance under model ambiguity. Insurance: Mathematics and Economics, 106, 128–145.] under squared-error divergence.

我们解决了保单买方和卖方之间的斯塔克尔伯格差分博弈，其中双方对可保损失都不清楚。买方和卖方都在外生随机范围内最大化他们的预期财富，加上反映模糊性的惩罚项。根据均值-方差溢价原理和衡量参与者模糊性的一般散度，我们半显式地获得了 Stackelberg 均衡。我们的主要结果是最优方差负载等于0并且卖方稳健的最优溢价规则等于买方的净溢价。的最优扭曲概率。这两个重要结果都概括了我们在 [Cao, J., Li, D., Young, VR & Zou, B. (2022) 中获得的结果。模型模糊下的保险 Stackelberg 微分博弈。保险：数学和经济学，106 , 128–145.] 在平方误差散度下。