The Optimal Strategy of Generalized Underwriting with the Variance Premium Principle for the Inclusive Health Insurance

A lot of inclusive health insurance projects have been brewing in many cities in China. Among them, ``\it WeiHuiBao'', which adopts a multi-layer reinsurance method that includes proportion, deductibles, and limit, has attracted our attention. We define such anunderwriting method with proportion, deductibles, and limit simultaneously as generalized underwriting method, which has never appeared as the optimal contract in existing literature but very common in reality. This paper aims at finding an optimal strategy in a two-layer generalized underwriting method. We solve two models, the optimal insurance model minimizing the premiums of policy-holders with the CTE of policy-holders' own risk less than an agreed threshold, and the optimal reinsurance model minimizing the VaR of insurer's total risk, under the variance premium principle, respectively. We find that the optimal contract forms of the two models support the clauses in ``\it WeiHuiBao'', and the numerical solutions under the Pareto distribution and the Gamma distribution are given. The underwriting form of ``\it WeiHuiBao'' is a multi-layer generalized underwriting method while this paper demonstrates the optimality of the two-layer underwriting method.