Research On Optimal Reinsurance And Investment Strategy For Insurers Under The Condition Of Risk Control

As a company providing risk protection,insurance companies have to bear the uncertainty of higher losses compared with other financial enterprises.In the process of dealing with risks,risk management and value preservation are the ways commonly used by insurance companies to determine the insurance strategy.For the Long-term development,on the one hand,in view of the difficulty of risk control caused by excessive insurance risk,insurance companies usually choose to purchase reinsurance to transfer part of the claim risk to the reinsurance company to disperse the risk.However,since reinsurance can be divided into proportional reinsurance and non-proportional reinsurance,how to choose the optimal strategy to achieve the optimal reinsurance purpose,requires the insurance company to design an optimal ratio for reinsurance.On the other hand,in order to realize the company’s profit and enhance the compensation ability,the insurance company also needs to implement the insurance investment,e.g.insurance premium value-added business.However,due to the temporal heterogeneity of the premium collection-and the inconsistency of the insurance cycle,the existing portfolio strategy does not meet the actual situation faced by insurance companies.Therefore,to maximize the long-term investment income for insurance companies,multi-period optimization problem of premiums portfolio needs to be further resolved.This paper starts from the perspective of controlling the operational risk of insurance companies,and establishes a set of investment probability and asset price thresholds,and constructs a series of mathematical physics equations such as dynamic programming equations as tools,and aims to ensure the long-term benefits of insurance companies.Design a set of insurance company investment strategy optimization programs to prevent operational risks,avoid investment risks,and reduce liquidity risks.The scheme includes the optimal reinsurance strategy of the insurance company under the market of the bull and bear market,the optimal excess loss investment strategy,the optimal portfolio reinsurance strategy and the optimal portfolio strategy,and is a package investment suggestion system under the uncertain market risk.Specifically,the main researches be summarized as follows:First,in the mean returning financial market,the reinsurer adopts the principle of variance premium,and its goal is to maximize the utility of the wealth at the end of the period.We discuss the optimal reinsurance and investment strategies in the case of the diffusion approximate claim model and the jump-diffusion claim model,respectively.Since the net profit condition is considered,the optimal reinsurance strategy is finally classified into three categories based on the calculated ratio of the optimal reinsurance strategy.According to the numerical simulation results,the optimal ratio reinsurance strategy will change when the claim amount is subordinated,and the investment strategy is the adjustment item affected by the parameters such as asset price,dividend and transaction rate.Second,we consider that the insurance company invests part of the surplus investment in the financial market and purchases the excess-of-loss reinsurance.The premium principle adopts the expectation premium principle.Under the utility maximization criterion,the optimal excess-of-loss reinsurance strategy of the diffusion approximate claim model is discussed.The results show that value function like the same proportion of reinsurance,the optimal reinsurance strategy in excess-of-loss reinsurance is also affected by the distribution of the claim amount,and the investment strategy is also the adjustment item affected by the parameters.Thirdly,we consider the combination of purchasing proportional reinsurance and excess loss reinsurance,the optimal reinsurance strategy and investment strategy under the diffusion approximate claim model and the jump-diffusion claim model are discussed respectively.The theorem shows that under some conditions,the total There is a pure excess-of-loss reinsurance strategy that is superior to any type of combined form reinsurance strategy and has the same conclusions under both claims models.Last,we use dynamic feedback control theory,and construct a new entropy model to describe system risk and non-system risk,and then propose an incremental-hybridYager’s entropy multi-period portfolio model with transaction cost,because the proposed model is a multi-objective problem,so the method of compromise planning is used to transform it into a single-objective problem.Then a compromise genetic algorithm is designed to solve the model.Finally,the numerical model is used to illustrate the proposed model compared with the traditional mean variance model.Have a better return.In the assumption of the financial market,in order to make the established mathematical model closer to the actual problem,some practical factors are also considered,so that the income model established on this basis is more reliable,so that the final result is generally operational.At the same time,some numerical experiments and diagrams are given to illustrate the validity and superiority of our conclusions.