Bowley solution of a variance game in insurance

Wenjun Jiang, Xiaoqing Liang and Virginia R. Young

Scandinavian Actuarial Journal, 2025, vol. 2025, issue 6, 617-634

Abstract: In this paper, we study a Stackelberg game for insurance contracting. Specifically, we assume that the insurance buyer and seller hold generalized mean-variance preferences and the premium is determined by a generalized variance premium principle. Under mild conditions, we derive the Bowley solution, which consists of the optimal indemnity and pricing functions, for the Stackelberg game. We also compare the Bowley solution with the Pareto optimal solution and prove that the Bowley solution can never be Pareto optimal. This finding shows the inefficiency of Stackelberg games in insurance contracting, which echoes the existing results derived in other settings. We present two specific examples to further show the implications of our main results as well as the sensitivity of the Bowley and Pareto optimal solutions with respect to the model parameters.

Date: 2025
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DOI: 10.1080/03461238.2024.2447468

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