Model Uncertainty, Ambiguity Aversion and Implications for Catastrophe Insurance Market

Uncertainty is the inherent nature of catastrophe models because people usually have incomplete knowledge or inaccurate information in regard to such rare events. In this paper we study the decision makers’ aversion to model uncertainty using various entropy measures proposed in microeconomic theory and statistical inferences theory. Under the multiplier utility preference framework and in a static Cournot competition setting, we show that reinsurers’ aversion to catastrophe model uncertainty induces a cost effect resulting in disequilibria, i.e., limited participation, an equilibrium price higher than the actuarially fair price, and possible market break-down in catastrophe reinsurance markets. We show that the tail behavior of catastrophic risks can be modeled by a generalized Pareto distribution through entropy minimization. A wellknown fact about catastrophe-linked securities is that they have zero or low correlations with other assets. However, if investors’ aversion to model uncertainty is higher than some threshold level, adding heavy-tailed catastrophic risks into the risk portfolio will have a negative diversification effect. JEL Classification: C0, C1, D8, G0, G2