Optimal Investment And Reinsurance Game Problems Under Model Uncertainty

In recent,years,the optimal investment and reinsurance problem has become a hot issue in the field of actuarial research.In the financial market,insurers need to make profits through investment portfolios to improve solvency.For risk management purposes,insurers sometimes need to transfer part of the claim risk to the reinsurer by signing reinsurance contract.s with the reinsurer to disperse their own risks.A reasonable reinsurance contract is an agreement made by an insurer and a reinsurer after reaching a consensus.Therefore,it needs to be considered from the perspective of both the insurer and the reinsurer.Since model uncertainty will bring adverse effects,the rational investors would like to adopt robust strategies to reduce the adverse effects of model uncertainty.Therefore,We formulate the investment-reinsurance Stackelberg differential game between the ambiguity averse insurer and the ambiguity averse reinsurer under model uncertainty.We consider the reinsurer and the insurer as the leader and the follower in the Stackelberg game model,which takes into account the interests of both parties.Firstly,we study the Stackelberg game problem of optimal investment and proportional reinsurance under the Heston’s SV model.An insurer and a reinsurer are both assumed to be able to invest in a risk-free asset and a risk asset,where the price process of the risky asset obeys Heston’s SV model.The goal of the insurer is to maximize the expected utility of its own terminal performance,and the goal of the reinsurer is to maximize the expected utility of its own terminal performance.It is assumed that insurance premium is calculated by the expected premium criterion,and no specific form of reinsurance premium is set.We apply stochastic control theory to solve the Hamilton-Jacobi-Bellman(HJB)equations for the insurer and reinsurer in turn to obtain the explicit expressions of the optimal equilibrium strategies and value functions.We also prove the verification theorem.We also analyze the efects of model parameters on the equilibrium strat.egies by numerical simulations,and give the corresponding econonic explanations.At the same time,we analyze the utility losses of the insurer and the reinsurer under the influence of model uncertainty theoretically.Afterwards,both the insurance and reinsurance premium are assumed to be calculated via the variance premium principle.We obtain the expressions for optimal equilibrium strategies and value functions.Finally,we compare the two results.Secondly.We construct a Stackelberg game model for optimal investment and proportional reinsurance under the mean-variance criterion considering the combined effects of model uncertaintv and delay effect.An insurer and a reinsurer are both assumed to be able to invest in a risk-free asset and a risk asset,where the price process of the risky asset obeys the GBM model.Considering the delay effect,SDDEs are used to characterize the wealth processes.We apply stochastic control theory to solve the extended HJB equations for the insurer and reinsurer in turn,and finally obtain the explicitexpressions of the optimal equilibrium strategies and value functions.This paper is devoted to making the models that are closer to the real situations,and trying to obtain the explicit expressions of the optimal equilibrium strategies and value functions.It provides a theoretical basis for optimal investment and reinsurance decisions.