In this paper, we consider a dynamic Pareto optimal risk-sharing problem under the time-consistent mean-variance criterion. A group of n insurers is assumed to share an exogenous risk whose dynamics is modelled by a Levy process. By solving the extended Hamilton-Jacobi-Bellman equation using the Lagrange multiplier method, an explicit form of the time-consistent equilibrium risk-bearing strategy for each insurer is obtained. We show that equilibrium risk-bearing strategies are mixtures of two common risk-sharing arrangements, namely the proportional and stop-loss strategies. Their explicit forms allow us to thoroughly examine the analytic properties of the equilibrium risk-bearing strategies. We later consider some extensions to the original model by introducing a set of financial investment opportunities and allowing for insurers' ambiguity towards the exogenous risk distribution. We again explicitly solve for the equilibrium risk-bearing strategies and further examine the impact of the extension component (investment or ambiguity) on these strategies.
个人简介：李丹萍，华东师范大学经济与管理学部统计学院副教授，主要研究方向为随机最优控制在金融和保险中的应用，目前已在Insurance: Mathematics and Economics, Journal of Economic Dynamics and Control, Scandinavian Actuarial Science等国际重要杂志上发表学术论文二十余篇。主持一项国家自然科学基金青年项目，2018年入选上海市晨光计划。