On Monopoly Insurance Pricing when Agents Differ in Risk Aversion

The paper analyzes a monopolistic insurer’s pricing strategies when potential customers differ in risk aversion and their type cannot be observed by the insurer. Our model builds on Schlesinger (1983), who derived optimal nonlinear pricing strategies for competitive and monopolistic insurance markets. While Schlesinger assumed existence, we are concerned with conditions under which optimal strategies may exist. We introduce a general model framework for continuous but not necessarily differentiable utility functions and derive conditions for existence of optimal insurance pricing strategies. An important application of our findings is “kinked” utility functions, which are found to offer a better match of actual decision making. Both fixed and proportionate premium loadings (relative to expected loss) are considered.