Agent-based Modeling and Simulation of Ambiguity in Catastrophe Insurance Markets

Pricing covers for catastrophes is challenging for insurers due to uncertainty in loss probabilities. This paper addresses this so-called ambiguity problem in competitive catastrophe insurance markets through three key approaches. First, it introduces ambiguity in premium pricing and capital holdings. Second, it develops an Agentbased Model simulator to mimic general insurance markets and the Lloyd's market. Third, it applies Empirical Game-Theoretical Analysis to explore insurers' ambiguity preferences in different markets. The study evaluates the effects of ambiguity by analyzing their impact on individual companies, differences between small and large companies, and overall market performance. Simulation results reveal that the simulator effectively captures underwriting cycles and insurers' strategic shifts following catastrophes. In markets with equally sized insurers, competition mitigates the negative effects of ambiguity by stabilizing premiums and increasing the number of underwritten risks. In markets with varying-sized insurers, large insurers gain market power while small insurers adopt aggressive ambiguity strategies to compete. In contrast, Lloyd's lead-follow mechanism encourages conservative ambiguity strategies and reduces bankruptcy.