Robust Insurance Pricing and Liquidity Management
Abstract
With the rise of emerging risks, model uncertainty poses a fundamental challenge in the insurance industry, making robust pricing a first-order question. This paper investigates how insurers' robustness preferences shape competitive equilibrium in a dynamic insurance market. Insurers optimize their underwriting and liquidity management strategies to maximize shareholder value, leading to equilibrium outcomes that can be analytically derived and numerically solved. Compared to a benchmark without model uncertainty, robust insurance pricing results in significantly higher premiums and equity valuations. Notably, our model yields three novel insights: (1) The minimum, maximum, and admissible range of aggregate capacity all expand, indicating that insurers' liquidity management becomes more conservative. (2) The expected length of the underwriting cycle increases substantially, far exceeding the range commonly reported in earlier empirical studies. (3) While the capacity process remains ergodic in the long run, the stationary density becomes more concentrated in low-capacity states, implying that liquidity-constrained insurers require longer to recover. Together, these findings provide a potential explanation for recent skepticism regarding the empirical evidence of underwriting cycles, suggesting that such cycles may indeed exist but are considerably longer than previously assumed.