In this paper,we analyze the relationship between the equilibrium reinsurance strategy and the tail of the distribution of the risk.Since Mean Residual Life(MRL)has a close relationship with the tail of the distributi...In this paper,we analyze the relationship between the equilibrium reinsurance strategy and the tail of the distribution of the risk.Since Mean Residual Life(MRL)has a close relationship with the tail of the distribution,we consider two classes of risk distributions,Decreasing Mean Residual Life(DMRL)and Increasing Mean Residual Life(IMRL)distributions,which can be used to classify light-tailed and heavy-tailed distributions,respectively.We assume that the underlying risk process is modelled by the classical CramérLundberg model process.Under the mean-variance criterion,by solving the extended Hamilton-Jacobi-Bellman equation,we derive the equilibrium reinsurance strategy for the insurer and the reinsurer under DMRL and IMRL,respectively.Furthermore,we analyze how to choose the reinsurance premium to make the insurer and the reinsurer agree with the same reinsurance strategy.We find that under the case of DMRL,if the distribution and the risk aversions satisfy certain conditions,the insurer and the reinsurer can adopt a reinsurance premium to agree on a reinsurance strategy,and under the case of IMRL,the insurer and the reinsurer can only agree with each other that the insurer do not purchase the reinsurance.展开更多
基金supported by the National Key R&D Program of China(2022YFA1007900)the National Natural Science Foundation of China(Nos.12271171,12171158,12071147,12001200)+3 种基金the Shanghai Philosophy Social Science Planning Office Project(Grant No.2022ZJB005)the Fundamental Research Funds for the Central Universities(2022QKT001)the State Key Program of National Natural Science Foundation of China(71931004)the Humanity and Social Science Foundation of Ningbo University(XPYB19002)。
文摘In this paper,we analyze the relationship between the equilibrium reinsurance strategy and the tail of the distribution of the risk.Since Mean Residual Life(MRL)has a close relationship with the tail of the distribution,we consider two classes of risk distributions,Decreasing Mean Residual Life(DMRL)and Increasing Mean Residual Life(IMRL)distributions,which can be used to classify light-tailed and heavy-tailed distributions,respectively.We assume that the underlying risk process is modelled by the classical CramérLundberg model process.Under the mean-variance criterion,by solving the extended Hamilton-Jacobi-Bellman equation,we derive the equilibrium reinsurance strategy for the insurer and the reinsurer under DMRL and IMRL,respectively.Furthermore,we analyze how to choose the reinsurance premium to make the insurer and the reinsurer agree with the same reinsurance strategy.We find that under the case of DMRL,if the distribution and the risk aversions satisfy certain conditions,the insurer and the reinsurer can adopt a reinsurance premium to agree on a reinsurance strategy,and under the case of IMRL,the insurer and the reinsurer can only agree with each other that the insurer do not purchase the reinsurance.
