Dynamic candidate-first aggregation for square-root experts

Develop a dynamic candidate-first barycenter for square-root stochastic-volatility experts by extending the Hamilton–Jacobi–Bellman or controlled martingale-problem framework to the degenerate volatility boundary at zero, including the necessary boundary analysis.

Background

The paper studies Cox–Ingersoll–Ross square-root variance factors, whose diffusion coefficient degenerates at the boundary where the variance reaches zero. It establishes a localized stationary information–transport divergence, existence of barycenters on compact parameter sets separated from the Feller boundary, and a fixed-variance noncommuting covariance selector.

The dynamic candidate-first aggregation theory developed earlier relies on uniform ellipticity. Consequently, it does not directly apply to a full square-root stochastic-volatility model up to the boundary. Resolving this limitation requires a degenerate Hamilton–Jacobi–Bellman treatment or an extension based on controlled martingale problems, together with an analysis of boundary behavior.