基于Kolmogorov-Arnold网络的巨灾债券定价
CAT Bond Pricing with Kolmogorov--Arnold Networks
- National University of Singapore（新加坡国立大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究针对复合泊松损失模型下的CAT债券定价问题，采用KAN结合基线加残差学习方法，提取符号定价公式并引入单调性约束，在90000个样本上实现0.483%的平均相对误差，实现了精度、速度与可解释性的平衡。
AI中文摘要：
我们研究在复合泊松损失模型（损失幅度服从对数正态分布）下，使用Kolmogorov-Arnold网络（KAN）对巨灾债券（CAT bond）价格的近似问题。基于基线加残差学习流程，我们对闭式对数正态基线价格的偏差训练KAN，并提取可解释的符号定价公式。该公式在90000个模拟价格的完全不相交保留样本上实现了0.483%的平均相对定价误差。与纯经验建模不同，我们还分析了真实CAT债券定价映射的结构特性，包括关于巨灾到达强度λ、初始短期利率r0和触发阈值D的单调性。我们推导了KAN边函数的充分条件，以保证学习模型能保留这些单调性，并构建了带收敛保证的单调性约束训练目标。结果表明，符号KAN替代模型在CAT债券估值的准确性、计算速度和可解释性之间提供了实用的折中方案。
英文摘要：
We study the approximation of CAT bond prices under a compound Poisson loss model with lognormal severities using Kolmogorov--Arnold Networks (KANs). Building on a baseline-plus-residual learning pipeline, we train a KAN on the deviation from a closed-form lognormal baseline price and extract an interpretable symbolic pricing formula. The extracted formula achieves an average relative pricing error of 0.483% on a fully disjoint holdout sample of 90,000 simulated prices. In contrast to purely empirical modelling, we also analyse structural properties of the true CAT bond pricing map, including monotonicity with respect to the catastrophe arrival intensity lambda, the initial short rate r0, and the trigger threshold D. We derive sufficient conditions on KAN edge functions that guarantee these monotonicities are preserved by the learned model, and formulate a monotonicity-constrained training objective with a convergence guarantee. Our results suggest that symbolic KAN surrogates provide a practical compromise between accuracy, computational speed, and interpretability for CAT bond valuation.
