Competitive insurance pricing with heterogeneous risks

This paper proposes a game-theoretic model that captures the interaction between price competition and risk heterogeneity in the insurance market. In this competitive game, each insurer sets a best-response premium to maximize the expected utility of its terminal wealth. We model heterogeneity between two distinct types of potential policyholders within a collective risk framework. We develop a Markovian structural demand model to capture how the expected number of policies is influenced by insurers’ premiums in a heterogeneous market. Within the non-cooperative game setting, we provide a sufficient condition to guarantee the existence of a pure-strategy Nash equilibrium. Several numerical examples, including a sensitivity analysis and repeated one-period myopic game extension, are provided to illustrate the implications of risk heterogeneity under competitive insurance pricing.