AI 中文总结
该研究将复合损失模型的贝叶斯后验近似转化为摊销问题，构建条件Wasserstein GAN，通过模拟校准等方法验证，成功近似多参数后验并应用于巨灾损失尾部风险分析。
AI 中文摘要
复合损失模型中的贝叶斯推断通常需要针对不同策略、市场场景和先验设定重复进行。在非共轭情况下，这可能需要重复的数值积分或马尔可夫链蒙特卡洛（MCMC）方法。我们将该问题表述为摊销后验近似，并构建了一个以充分统计量、先验均值、变异系数以及先验族混合权重为条件的条件Wasserstein生成对抗网络。值得注意的是，单个共享生成器能够近似泊松强度和帕累托形状参数在伽马、逆高斯和对数正态先验混合下的后验分布。我们通过基于模拟的校准以及与解析后验、确定性求积和大量MCMC模拟的比较来评估近似效果。在对极端自然灾害损失数据的应用中，我们生成了滚动一年期后验预测分布，并研究了重尾严重性和先验族不确定性对总尾部风险的影响。
英文摘要
Bayesian inference in compound loss models must often be repeated across policies, market scenarios, and prior specifications. Outside conjugate cases, this may require repeated numerical integration or Markov chain Monte Carlo (MCMC). We formulate this problem as amortized posterior approximation and construct a conditional Wasserstein generative adversarial network conditioned on sufficient statistics, prior mean and coefficient of variation, and mixture weights of prior families. Notably, a single shared generator is able to approximate the posterior laws of both the Poisson intensity and the Pareto shape parameter under mixtures of Gamma, inverse-Gaussian, and lognormal priors. We assess the approximation by simulation-based calibration and by comparisons with analytical posteriors, deterministic quadrature, and extensive MCMC simulations. In an application to data on extreme natural catastrophe losses, we produce rolling one-year posterior predictive distributions, and examine the effects of heavy-tailed severity and prior-family uncertainty on aggregate tail risk.
