Price competition in general insurance markets: a dynamic game-theoretic approach

In the insurance markets, the number of product-specific policies from different companies has increased significantly. The strong market competition has boosted the demand for a competitive premium. In actuarial science, scant literature still exists on how competition actually affects the calculation and the pricing cycles of company's premiums. In this paper, we model premium dynamics via a differential game, and study the insurers' equilibrium premium pricing in a competitive market. We apply an optimal control theory approach to determine the open-loop strategies Nash Equilibrium premiums.

Two models are investigated. The market power of each insurance company is characterized by a price sensitive parameter, and the business volume is affected by the solvency ratio. Considering the average market premiums, the first model studies an exponential relation between premium strategies and volume of business. The other model initially characterize the competition between any selected pair of insurers, then aggregates all the paired competitions in the market. A numerical example illustrates the premium dynamics, and shows that premium cycles may exist in equilibrium.

This is a joint work with Tim J. Boonen (University of Amsterdam) and Renchao Wu (University of Liverpool)