A Mean Field Game Approach to Optimal Investment and Risk Control for Competitive Insurers

We consider an insurance market consisting of multiple competitive insures with a mean filed interaction via their terminal wealths under the exponential performance. It is assumed that each insurer regulates her risk by controlling the number of polices. We respectively establish the constant Nash equilibrium (independent of time) on the investment and risk control strategy for finite n-insurer and the constant mean field equilibrium for the corresponding mean field game (MFG) problem (when the number of insurers tends to infinite). We examine the convergence relationship between the constant Nash equilibrium of finite-n insurer and the mean field equilibrium of the corresponding MFG game