Equilibrium insurance pricing for large losses

Abstract

Catastrophe‐exposed P&C insurance markets increasingly confront low‐frequency but high‐severity losses. When such risks interact with costly external financing, insurance pricing depends not only on expected losses but also on insurers' balance‐sheet conditions and capacity constraints. In this paper, we develop a dynamic competitive equilibrium framework of insurance capacity and pricing under jump‐diffusion risk and model uncertainty. We show that catastrophe jumps introduce a liability‐side gamble‐for‐resurrection mechanism through the interaction of limited liability and recapitalization options, which can generate non‐monotonic and non‐smooth pricing patterns under certain conditions. Robustness concerns raise equilibrium prices and capital buffers while attenuating excessive risk‐taking incentives. Using a market‐disciplined calibration, we show that jump risk generates substantial pricing effects beyond expected losses alone and shapes the duration of endogenous underwriting cycles.