ASRM Seminar Series

Title:
Amortized Bayesian Inference for High Quantiles: QuantilePFN

Abstract:
Accurate estimation of extreme high quantiles is central to Value-at-Risk (VaR) assessment and solvency regulation in insurance and finance, yet it remains notoriously difficult in data-scarce settings. Classical Extreme Value Theory (EVT) methods rely on asymptotic approximations that can be unstable in small to moderate samples. Moreover, procedures such as POT-GPD require subjective threshold selection, leading to substantial bias–variance trade-offs and sensitivity to tuning choices. We introduce QuantilePFN, a novel framework for high-quantile estimation based on amortized Bayesian inference via Prior-Fitted Networks (PFNs). The method pre-trains a Transformer model on a rich hierarchical generative prior constructed from Gamma-Scaled Phase-Type (PH) distributions. Through this pre-training, the network learns an inductive bias that captures realistic tail behaviors of heavy-tailed risks. Once trained, QuantilePFN performs end-to-end inference directly on raw datasets, automatically adapting to tail structure without manual thresholding or parameter tuning. Extensive benchmarking across a broad collection of heavy-tailed distributions shows that QuantilePFN consistently achieves lower mean absolute error (MAE) and mean squared error (MSE) than optimized POT-GPD and Hill estimators for sample sizes up to 1,000. These results suggest that QuantilePFN provides a principled and automated alternative for high-quantile estimation in limited-data regimes. This is joint work with Ph.D. students Yuqi Jing and Daniel Zhang (University of Waterloo).

Speaker's Bio:
Chengguo Weng is a Full Professor in the Department of Statistics and Actuarial Science at the University of Waterloo, where he has been a faculty member since 2010. He received his Bachelor’s and Master’s degrees in Statistics from Zhejiang University and his PhD in Actuarial Science from the University of Waterloo. His research focuses on actuarial risk management and quantitative finance, with particular interests in insurance design, portfolio optimization, and various machine learning applications in insurance and finance. His paper entitled “Optimal reinsurance under VaR and CTE risk measures” has remained among the 50 most cited papers published in Insurance: Mathematics and Economics, according to CitEc, every year since 2016.