Proves finite moments E[S_T^p] < ∞ for p < p_ρ in rough Bergomi under ρ ∈ [-1,0) and positive atom at zero for rough Heston variance process.
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11 Pith papers cite this work. Polarity classification is still indexing.
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For regular Volterra kernels the square-root process obeys a time-dependent Feller condition and stays positive; for rough regularly-varying kernels it hits zero with positive probability and carries an atom at the boundary.
Establishes finite-sample MSE bounds separating discretization and fluctuation errors for expected signature estimation under summable block-signature covariance, applicable to fractional Ornstein-Uhlenbeck processes across Hurst regimes.
Rough-path market models satisfying no-controlled-free-lunch reduce admissible drivers to Itô lifts of Brownian motion (up to time change) once signature-type strategies are allowed.
Develops a Hilbert space-valued Markovian lift framework for stochastic Volterra equations and establishes existence of limit distributions, LLN with convergence rate, and CLT for time averages in the Gaussian domain.
Constructs QMLE for drift parameter in singular Volterra SDE with small diffusion, proving path reconstruction error O(h^{1/2}) independent of roughness α and yielding efficient estimator as ε→0.
Extends rough fractional stochastic volatility to a multivariate fOU model with GMM estimation, simulation validation, and empirical analysis of realized volatility series showing correlations and spillover effects.
Bayesian joint estimation of Hurst parameter and volatility in fractional SDE models is developed to propagate parameter uncertainty into fractional Black-Scholes option prices.
Develops a singular stochastic control model for optimal execution with stochastic resilience dynamics and regime-switching liquidity, proving the value function is the unique viscosity solution to a system of variational HJB inequalities.
Constructs a consistent and asymptotically normal trajectory fitting estimator for the drift parameter θ* in singular-kernel stochastic Volterra equations under small-noise asymptotics.
Derives a generalized European option pricing PDE from an operational-time log-price lattice with state-dependent transitions that converges to the Black-Scholes-Merton PDE under risk-neutral drift and constant volatility.
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Moments in Rough Bergomi and Boundary Attainment in Rough Heston
Proves finite moments E[S_T^p] < ∞ for p < p_ρ in rough Bergomi under ρ ∈ [-1,0) and positive atom at zero for rough Heston variance process.
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Boundary behaviour of the Volterra square-root process
For regular Volterra kernels the square-root process obeys a time-dependent Feller condition and stays positive; for rough regularly-varying kernels it hits zero with positive probability and carries an atom at the boundary.
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Limit theorems for stochastic Volterra processes
Develops a Hilbert space-valued Markovian lift framework for stochastic Volterra equations and establishes existence of limit distributions, LLN with convergence rate, and CLT for time averages in the Gaussian domain.