Insurance Contracts, As Two-Person Games

In this paper, the problem of completing a contract between a buyer and a seller of insurance is presented as a two-person, zero-sum game, and previous results concerning optimal insurance contracts are reviewed from the viewpoint of game theory. While this point of view seems unrealistic, it is seen to lead to theorems which involve contracts actually encountered in the real world. It is shown that an insurance agreement which splits each loss proportionately between the insurer and the insured is optimal from the viewpoint of a risk averting insurance company that seeks to maximize its expected utility when the net insurance premium is fixed.