提出公平定价连续体框架,平衡精算与社会公平。
α-Fair Insurance Pricing: A Fairness Continuum

- 用参数α控制精算与社会公平的权衡,实现跨群体补贴约束。
- 在各风险组内设定补贴预算,确保保费可承受且保险可持续。
- 适合关注监管合规与公平性平衡的保险政策制定者。
保险定价中的公平性长期存在争议:一方面,保险公司为追求利润,依据个体风险差异设定差异化保费以实现精算公平;另一方面,保险具有社会共担风险的功能,需通过组间补贴促进社会团结公平。两者之间的张力使定价复杂化,尤其在数据精细、监管压力增大的现代背景下。为此,我们提出α-公平个体偿付保费(α-FISP)框架,显式建模精算公平与社会公平间的权衡,并保证偿付能力这一保险运营的基本要求。将定价问题建模为带约束的优化问题,对精算保费进行调整,受限于每类风险组内的补贴预算。该方法自然生成一个由α参数化的解族,描绘出从纯精算到纯社会公平的连续路径,使决策者可选择合适的公平度点。理论分析证明了框架的合理性。数值实验表明,α-FISP计算高效,且与美国各州异质性的监管要求高度契合。
原文摘要 · Abstract (English)
Fairness in insurance pricing remains a long-standing and deeply debated puzzle. On one hand, insurers, driven by profitability considerations, set premiums that differentiate across individual risks to achieve actuarial fairness. On the other hand, insurance serves a critical societal function by pooling risks across a population, motivating cross-subsidization among groups to promote solidarity fairness. The tension between these two competing notions of fairness makes insurance pricing inherently complex, particularly in modern settings where granular data allow for increasingly fine risk differentiation and regulators face growing pressure to protect vulnerable groups. To address this challenge, we propose an $α$-\textbf{F}air \textbf{I}ndividual \textbf{S}olvent \textbf{P}remium ($α$-FISP) framework for insurance pricing that explicitly captures the trade-off between actuarial and solidarity fairness while guaranteeing solvency, a fundamental requirement in insurance operations. We formulate the pricing problem as a constrained optimization task, where actuarially fair premiums are adjusted subject to budget constraints on cross-subsidization within each risk class. This formulation naturally yields a family of solutions parameterized by $α$, tracing a continuum between purely actuarial and purely solidarity-based pricing and enabling decision-makers to select an operating point along this fairness spectrum. We derive theoretical guarantees for the proposed framework. Numerical experiments show that $α$-FISP is computationally tractable and aligns well with the U.S. regulatory regimes featuring heterogeneous state-level fairness requirements.
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