A reinsurance and investment game between two insurance companies with the different opinions about some extra information

The work studies a reinsurance and investment game between two insurance companies which have different opinions about some extra information. We assume that the goal of each insurance company is to maximize its utility of the difference between its terminal surplus and that of its competitor at the terminal time T. Moreover, at the beginning of the game, two insurance companies acquire some information about the future realization of the claims process. However, they treat with it differently, since one company trusts it while its competitor does not. Our focus is to study how the companies are affected by this information. By utilizing the dynamic programming principle and the enlargement of filtration techniques, the existence of the Nash equilibrium solutions can be verified. For the exponential utility, we derive three kinds of the candidate forms for the equilibrium strategies in the special situations and also provide the numerical method for the general situation. Some numerical examples are presented to illustrate how the reinsurance strategies change when the information level and other parameters vary.