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Ruimeng Hu, Byungdoo Kong · 2026-06-25
The paper builds a mathematical model of how a single dominant reinsurer sets prices when selling coverage to many different insurance companies, where each insurer decides how much risk to keep versus pass on, partly based on how it compares to peers. It solves for the resulting equilibrium prices and retention choices in both a finite number of insurers and a large-population (mean field) limit, and shows those equilibria may not be unique.
Why it matters: For those analyzing insurance or reinsurance firms, it offers a structured way to think about how reinsurance premiums, competitive dynamics, and peer-comparison behavior interact to shape how much risk insurers actually retain. It may help contextualize why insurers sometimes retain risk even when ceding it looks cheap, though the work is theoretical.
⚠ This is a stylized theoretical/mathematical model with numerical illustrations, not an empirical study or tradable strategy, so its assumptions may not match real markets.
We study endogenous reinsurance pricing in a competitive insurance market with one strategic reinsurer and many heterogeneous insurers. The reinsurer acts as a Stackelberg leader by choosing a common premium rate and an investment strategy, while insurers decide how much risk to retain and how to invest, taking into account their own performance, their performance relative to the insurer population, and common insurance-claim and financial-market noise. This creates a feedback loop absent from standard reinsurance models with exogenous premiums: a premium change affects insurers directly through the cost of reinsurance, and indirectly through the population's aggregate exposure to common insurance-claim risk. For a fixed premium, we characterize the insurers' equilibrium retention through a scalar fixed point and establish its monotone premium response. This characterization reveals a spillover mechanism generated by relative performance concerns and leads to a threshold structure in which insurers move from full cession to partial retention and then to full retention as the premium increases. Using this structure, we reduce the reinsurer's premium problem to a one-dimensional optimization over a compact premium interval and characterize Stackelberg equilibria in both finite-player and mean field models. In the finite-player case, we develop an efficient threshold continuation procedure that determines equilibrium premiums without enumerating all retention configurations. We also prove convergence from finite-player equilibria to mean field equilibria without requiring the mean field equilibrium premium to be unique. Numerical illustrations show how relative performance concerns amplify spillover effects and can induce retention even when reinsurance remains actuarially favorable. They also demonstrate that Stackelberg equilibria need not be unique in either setting.
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AI summary generated from the paper’s public abstract via arXiv; it may miss nuance — read the source before relying on it. Thank you to arXiv for its open-access interoperability; StockTools is not affiliated with arXiv, and all rights remain with the authors. Educational only, not financial advice.