Boundary Behaviour of the Volterra Square-Root Process

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The paper provides foundational theoretical results for rough volatility models (rough Heston, Volterra Heston) which are widely used in quantitative finance for derivative pricing and risk management. The results on boundary behavior (hitting zero, negative moments) directly impact the well-posedness of these models. The equivalent martingale measure analysis is crucial for pricing theory. However, the paper is primarily theoretical and does not provide direct trading algorithms or empirical implementations. The severe restrictions on drift specifications in the rough case have practical implications for model calibration and hedging.

The paper is highly theoretical with advanced mathematics including: generalized Riemann-Liouville fractional calculus, Volterra integral equations, comparison principles, bootstrapping arguments, regularly varying functions, Karamata's Tauberian theorem, Potter's bounds, and affine transformation formulas. Implementation would require deep expertise in stochastic analysis and fractional calculus. The numerical bounds in Table 1 are straightforward to compute, but the theoretical framework is extremely sophisticated.

The paper is purely theoretical with complete proofs provided. All mathematical arguments are self-contained with detailed derivations. No numerical experiments or code are required for verification. The numerical table (Table 1) provides concrete parameter values for illustration. However, the proofs are highly technical and require expertise in stochastic analysis, Volterra equations, and fractional calculus.