Abstract
This paper presents a novel approach to optimizing profit margins in non-life insurance markets through a gradient descent-based method, targeting three key objectives: 1) maximizing profit margins, 2) ensuring conversion rates, and 3) enforcing fairness criteria such as demographic parity (DP). Traditional pricing optimization, which heavily lean on linear and semi definite programming, encounter challenges in balancing profitability and fairness. These challenges become especially pronounced in situations that necessitate continuous rate adjustments and the incorporation of fairness criteria. Specifically, indirect Ratebook optimization, a widely-used method for new business price setting, relies on predictor models such as XGBoost or GLMs/GAMs to estimate on downstream individually optimized prices. However, this strategy is prone to sequential errors and struggles to effectively manage optimizations for continuous rate scenarios. In practice, to save time actuaries frequently opt for optimization within discrete intervals (e.g., range of [-20\%, +20\%] with fix increments) leading to approximate estimations. Moreover, to circumvent infeasible solutions they often use relaxed constraints leading to suboptimal pricing strategies. The reverse-engineered nature of traditional models complicates the enforcement of fairness and can lead to biased outcomes. Our method addresses these challenges by employing a direct optimization strategy in the continuous space of rates and by embedding fairness through an adversarial predictor model. This innovation not only reduces sequential errors and simplifies the complexities found in traditional models but also directly integrates fairness measures into the commercial premium calculation. We demonstrate improved margin performance and stronger enforcement of fairness highlighting the critical need to evolve existing pricing strategies.
Abstract (translated)
本文提出了一种通过梯度下降方法优化非寿险市场利润率的新方法，旨在实现三个关键目标：1）最大化利润率，2）确保转换率，3）强制执行公平标准，如人口平等（DP）。传统的定价优化方法过于依赖线性和半定理规划，在平衡盈利和公平方面存在挑战。特别是在需要连续调整速率和公平标准的情况下，这些挑战变得更加突出。具体来说，间接率簿优化，一种广泛用于新业务价格设置的方法，依赖于预测模型如XGBoost或GLMs/GAMs来估计下游的个体优化价格。然而，这种策略容易产生序列误差，且在处理连续速率场景的优化时表现不佳。在实践中，为了节省时间， Actuaries经常在离散区间内进行优化（例如，范围为[-20%, +20%]，固定步长），导致近似估计。此外，为了绕过无解问题，他们通常使用放松的约束条件，导致不公平定价策略。传统模型的反向工程性质使得公平和执行变得更加复杂，可能导致偏差结果。我们的方法通过在连续利率的领域采用直接优化策略来解决这些挑战。通过将公平通过对抗性预测器模型嵌入其中，这种创新不仅减少了序列误差，简化了传统模型的复杂性，而且将公平度措施直接整合到商业保单计算中。我们证明了提高边际表现的改进效果，并强调了必须改革现有定价策略的关键必要性。
URL
https://arxiv.org/abs/2404.10275
