AI and the World's Hard Problems · Mathematics · arXiv · 2026-10-26
On the continuity of conditional distributions and stratification for derivative pricing
Stratification reduces Monte Carlo estimator variance, but its benefit depends on choosing a good low-dimensional stratification factor, which is hard to find in complex continuous-time models. The authors study constructing such factors with neural networks for derivative pricing under proportional allocation. They prove continuity results for conditional expectations and distributions, give a universal approximation theorem for admissible factors, and show counterexamples that mark the limits of this continuity theory. In numerical experiments on a constant-maturity-swap range accrual and a worst-of autocallable, the learned factors outperformed all benchmarks considered.