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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Quantitative Finance , volume =
10 Pith papers cite this work. Polarity classification is still indexing.
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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.
For regular Volterra kernels the square-root process avoids zero under a time-dependent Feller condition while rough regularly-varying kernels force an atom at zero, with the limit law still having finite negative exponential moments; equivalent martingale measures in the Volterra Heston model exist
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.
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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Unbiased Rough Integrators and No Free Lunch in Rough-Path-Based Market Models
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.
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Optimal Execution under Liquidity Uncertainty
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.