Strong-solution existence for singular-kernel Volterra Heston equations

Establish the existence of a strong solution for the Volterra Heston stochastic Volterra equation with sufficiently singular fractional kernels, including kernels corresponding to rough-volatility regimes for which the factor process may fail to be a semimartingale.

Background

The paper considers Volterra Heston factor processes driven by kernels that can be sufficiently singular, including fractional kernels. For such kernels, the factor process need not be Markovian or a semimartingale, and the authors work with weak solutions or a common filtration rather than assuming a strong solution. Establishing strong existence would provide a stronger pathwise foundation for these models and would permit their treatment within the Brownian-filtration framework discussed later in the paper.

The same unresolved issue is cited as a reason for using the more general predictable-representation and immersion assumptions in the integrated-variance-clock framework. The paper does not resolve strong existence for these singular-kernel equations.