Paper: arXiv 2510.15709

Authors: Shunzhi Pang

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.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 3.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous theoretical dynamic general equilibrium model using HJBI equations and robust control under ambiguity. While it delivers clear novel insights regarding the length and asymmetry of insurance underwriting cycles, it relies on calibrated numerical solutions rather than empirical backtesting or statistical validation on real-world data.

Research Flowchart

  flowchart TD
    A[Research Goal: Evaluate impact of robustness preferences & model uncertainty on insurance pricing & liquidity] --> B[Model Setup & Inputs: Dynamic competitive market, emerging risks, liquidity constraints]
    B --> C[Optimization Process: Solve joint underwriting & liquidity management for shareholder value]
    C --> D[Equilibrium Derivation: Analytical & numerical solution for robust market equilibrium]
    D --> E1[Finding 1: Higher insurance premiums & equity valuations]
    D --> E2[Finding 2: Expanded capacity range & more conservative liquidity management]
    D --> E3[Finding 3: Longer underwriting cycles & slower recovery from low-capacity states]

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1 of 98 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.