Mean field and n-insurers games for robust optimal reinsurance-investment in correlated markets

The paper investigates a family of robust reinsurance-investment strategies under relative performance criteria for the insurers who have exponential utility and trade in a common reinsurance-investment horizon in log-normal markets. Assume that two correlated Brownian motions used to characterize the insurance surplus risk and stock price risk. By applying stochastic control theories, we derive the closed-form solutions for the n-players game and the corresponding mean field game, furthermore the equilibria strategies are shown to be unique in the class of constant equilibria. Finally, we present the influence of model parameters on reinsurance and investment strategies with economic explanations by some numerical figures.