In this paper, we compute the Bowley solution of a one-period, mean–variance Stackelberg game in insurance, in which a buyer and a seller of insurance are the two players, and they act in a certain order. First, the seller offers the buyer any (reasonable) indemnity policy in exchange for a premium computed according to the mean–variance premium principle. Then, the buyer chooses an indemnity policy, given that premium rule. To optimize the choices of the two players, we work backwards. Specifically, given any pair of parameters for the mean–variance premium principle, we compute the optimal insurance indemnity to maximize a mean–variance functional of the buyer’s terminal wealth. Then, we compute the parameters of the mean–variance premium principle to maximize the seller’s expected terminal wealth, given the foreknowledge of what the buyer will choose when offered that premium principle. This pair of optimal choices, namely, the optimal indemnity and the optimal parameters of the premium principle, constitute a Bowley solution of this Stackelberg game. We illustrate our results via numerical examples.

在本文中，我们计算了保险费时的一期均值方差Stackelberg博弈的Bowley解，其中保险的买者和卖者是两个参与者，并且它们以一定的顺序起作用。首先，卖方向买方提供任何（合理）赔偿政策，以换取根据均值-方差保费原则计算的保费。然后，购买者根据给定的保险费规则选择赔偿政策。为了优化这两家公司的选择，我们倒退了。具体来说，给定均值-方差保费原则的任何一对参数，我们将计算最佳保险赔偿金，以最大化买方最终财富的均值-方差函数。然后，我们计算均值-方差溢价原理的参数，以最大化卖方的预期最终财富，考虑到买方会提供该溢价原则时会选择什么。这对最优选择，即最优赔款和保费原则的最优参数，构成了此Stackelberg游戏的Bowley解决方案。我们通过数值示例来说明我们的结果。