Optimal Reinsurance-investment Research For Insurers And Reinsurers Under Jump Diffusion Risk Model

Risk management is an important subject for insurers and reinsurers.Reinsurance is a form of insurance.It is an insurance purchased by insurers in order to transfer risks and reduce the pressure of risks.Investment can make insurers plan their surplus reasonably,and make them get more income to improve their solvency.In recent years,many experts have made in-depth research on the optimal reinsurance investment strategy.On this basis,we have mainly made the following two aspects of research.Firstly,the paper studies the joint optimal reinsurance-investment strategy of reinsurance under variable interest rate.Under the condition of variable interest rate,based on the jump-diffusion risk model,the optimal reinsurance-investment model framework for insurers and reinsurers is established.Among them,insurers and reinsurers are allowed to invest in risk-free assets and risk assets.It is assumed that the risk-free interest rate is characterized by the deterministic interest rate function,while the price of risk assets is characterized by the GBM(Geometric Brownian Motion)model.The HJB(Hamilton-Jacobi-Bellman)equations are established and solved by applying the principle of dynamic programming and dual theory.Then,through the interest game between the insurer and reinsurer,the two sides reach a consensus and get the optimal reinsurance-investment strategy.Finally,the sensitivity analysis and economic explanation of correlation coefficient are carried out by numerical simulation.Secondly,under the jump-diffusion risk model,the optimal investment and reinsurance strategies of insurers and reinsurers with European call options are studied.With the goal of maximizing the terminal wealth utility of both insurers and reinsurers,the numerical solution of the optimal investment-reinsurance strategy including options is obtained by using the dynamic programming principle and dual theory.Then,the hedging model of reinsurance investment of both insurers and reinsurers is established,and the two strategies are compared.Finally,the influence of each parameter on the optimal strategy is analyzed.Finally,we summarize and look forward to the full text,and combine the shortcomings of this paper to give some further research and improvement of the direction.