Aleksandar Arandjelovic, Pavel V. Shevchenko, George Tzougasq-fin.RM stat.ML
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.
Automated Driving System deployments create a foundational ratemaking challenge: sparse experience, shifting operational design domains, and non-stationary risk across software releases. We propose a hierarchical Bayesian credibility framework pooling across cities, software versions, and territories via a learned ODD-similarity kernel, nesting Buhlmann-Straub as a limiting case. Demonstrated on 648 verified-engaged Waymo crashes across four U.S. metros from the NHTSA Standing General Order database against 116 million matched miles, city-aggregate credibility weights are moderate (0.12-0.46), partial pooling decisively outperforms no pooling, and a power analysis shows the learned kernel's advantage becomes detectable at approximately twelve deployed cities.