Bin Li (University of Waterloo)

Optimal dynamic risk sharing under the time-consistent mean-variance criterion

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 modeled by a Levy process. By solving the extended Hamilton-Jacobi-Bellman equation and utilizing the Lagrangian method, an explicit form of the equilibrium bearing function for each insurer is obtained. We show that the equilibrium bearing functions are mixtures of two common risk sharing strategies, namely the proportional and stop-loss strategies. Thanks to their explicit forms, analytic properties of the equilibrium bearing functions are thoroughly examined. We later consider three extensions to the original model by adding one of the following features: a risk sharing constraint on the insurers, a set of financial investment opportunities, and the insurers' ambiguity towards the exogenous risk. For these extended models, the equilibrium bearing functions are once again explicitly solved, and the impact of the constraint, investment, and ambiguity component on the bearing functions are further examined. We conclude the paper by applying our results to the classical risk sharing problem in a pure exchange economy