Self-protection, insurance demand and cost-sharing strategy under mean-variance preferences

This article studies a mean-variance Stackelberg game between an insured and an insurer under a self-protection model, where the insured's effort is observable by the insurer and reflected in the insurance premium. We adopt a proportional insurance model under a quadratic premium principle and incorporate a cost-sharing mechanism for self-protection. The existence of equilibrium solutions for insurance demand, self-protection effort, and cost-sharing proportions is established, and their interactions are analyzed theoretically. Numerical analysis reveals conditions under which self-protection and market insurance act as complementary or substitutable risk management tools.