Discrete dynamical Pareto optimization model in the risk portfolio for natural disaster insurance in China

Disaster insurance is an effective way in reducing and sharing natural disaster risk. In this paper, a special risk management model based on the cooperative insurance among the operating governments, insurance market and public is proposed. Firstly, we divided the study areas into units. In each unit, we analyze the risk stochastic process of the insurers and the operating governments, the latter providing the policy support and the subsidy. Secondly, the processes of the fixed risk initial value, the premium income, the transaction cost and the claim are all considered in the risk stochastic process of the insurers. In the risk stochastic process of the public, we consider the pure income after claim and the subsidy from the operating governments. Then, we introduce the ruin probability and stable operation of insurers, the stopping time of the ruin probability and the recovery capability of the public. The risk portfolio stochastic optimal model, which shows that each party can effectively participate in this management model, is established in order to ensure the equilibrium between the insurance supply and demand. The ruin probability, stability of insurance market and the recovery capability of the public are considered completely in this model. Finally, we conduct numerical simulation to verify the results of the models.