This paper formulates and studies a stochastic maximum principle for forward-backward stochastic Volterra integral equations (FBSVIEs in short), while the control area is assumed to be convex. Then a linear quadratic (LQ in short) problem for backward stochastic Volterra integral equations (BSVIEs in short) is present …
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48 results for “Backward stochastic Volterra integral equations”
Paper develops methods for solving complex stochastic equations using Malliavin calculus.
problem Existence, uniqueness, and regularity of solutions to BSVIEs.
method Malliavin calculus for tackling diagonal processes and nonlinear dependence.
result Developed well-posedness results for BSVIEs, including probabilistic interpretation of PDEs and portfolio optimization.
Deep-learning method solves BSVIEs and coupled systems.
problem High-dimensional, time-inconsistent stochastic control problems.
method Trains a neural network to approximate solution fields directly.
result Non-asymptotic error bound and scalable performance.
We link SVEs to SPDEs and derive Kolmogorov equations for singular kernels.
problem Solving stochastic Volterra equations with singular kernels.
method Establishing connections between SVEs and SPDEs, using stochastic calculus in Hilbert spaces.
result Solutions of SVEs can be expressed in terms of backward Kolmogorov equations.
Paper introduces cubature method for stochastic Volterra equations.
problem Solving stochastic Volterra integral equations efficiently.
method Derive stochastic Taylor expansion, introduce cubature measure.
result Cubature method is more efficient than Euler scheme under certain conditions.
Simulating integrated Volterra square-root processes and Volterra Heston models via Inverse Gaussianq-fin.MF
A new simulation method for Volterra processes improves convergence for rough kernels.
problem Simulating Volterra processes with singular kernels.
method iVi (integrated Volterra implicit) scheme based on Inverse Gaussian distribution.
result The iVi scheme achieves weak convergence with few time steps, especially for rough kernels.
This research improves deep neural networks for parameter identification and prediction in stochastic Volterra integral equations.
problem Parameter identification and prediction in Volterra integral equations driven by Gaussian noise.
method Improved deep neural networks framework that incorporates inter-output relationships into the loss function.
result The framework enhances parameter estimation accuracy and provides accurate solutions for modeling stochastic systems.
Study proves optimal controls for stochastic Volterra equations with singular kernels.
problem Existence of optimal controls for stochastic Volterra equations with singular kernels.
method Sufficient conditions based on integrability and growth hypotheses.
result Existence of optimal relaxed and strict controls under classical convexity assumptions.
Study small-time CLTs for stochastic Volterra equations with various kernels.
problem Understanding the behavior of stochastic Volterra equations with different kernels.
method Proved convergence of finite-dimensional distributions, functional CLT, and limit theorems for smooth transformations.
result Derived asymptotic pricing formulae for digital calls in rough volatility models.
Investigates mean-variance portfolio selection in non-Markovian markets.
problem Continuous-time Markowitz mean-variance portfolio selection in fake stationary affine Volterra models.
method Stochastic factor solution to a Riccati BSDE, deriving explicit solutions as multi-dimensional Riccati-Volterra equations.
result Analytical closed-form expressions for optimal portfolio policies and mean-variance efficient frontier.
The paper analyzes the stationarity of stochastic Volterra integral equations and introduces fake stationary regimes.
problem Analyzing the stationarity of non-Markovian dynamical systems described by SVIEs.
method Investigates the properties of SVIE solutions, focusing on stationarity over finite and long time horizons, and introduces a deterministic stabilizer to induce a fake stationary regime.
result SVIEs do not exhibit a strong stationary regime unless the kernel is constant or degenerate, but a fake stationary regime can be achieved with a deterministic stabilizer.
Paper solves Merton's portfolio problem in a non-Markovian, non-semimartingale model.
problem Merton's portfolio optimization in a fake stationary Volterra-Heston model.
method Stochastic factor solution to a Riccati BSDE, combined with martingale optimality principle.
result Derives semi-closed form optimal strategies and value function.
We provide existence, uniqueness and stability results for affine stochastic Volterra equations with -kernels and jumps. Such equations arise as scaling limits of branching processes in population genetics and self-exciting Hawkes processes in mathematical finance. The strategy we adopt for the existence part is b…
Optimal liquidation strategy with price impact and signal exploitation.
problem Maximizing revenue-risk in a market with transient and temporary price impact.
method Infinite dimensional stochastic control approach, backward stochastic differential equation, operator-valued Riccati equation.
result Explicit expression for the optimal trading strategy.
This paper optimizes portfolio selection for multivariate affine and quadratic Volterra models with rough volatilities.
problem Optimizing portfolio selection for multivariate models with rough volatilities and stochastic correlations.
method Investigates continuous-time Markowitz mean-variance problem for multivariate affine and quadratic Volterra models using Riccati backward stochastic differential equations (BSDEs).
result Derives explicit solutions for BSDEs in affine Volterra models and new analytic formulae for quadratic models.
This work studies nonnegativity-preserving kernels for stochastic equations and their applications.
problem Nonnegativity preservation in stochastic Volterra equations and related processes.
method Characterization and application of completely monotone kernels; approximation schemes for weak error.
result Positive linear combinations of decaying exponentials can be used for second-order approximation schemes.
Investigates optimal investment strategies in financial markets with jumps.
problem Optimal portfolio selection for investors in multi-asset financial markets with jumps.
method Uses martingale optimality principle and Riccati backward stochastic differential equations with jumps.
result Derives semi-closed form optimal strategies and value function for Merton's problem.
Pathwise uniqueness shown for specific stochastic equations.
problem Stochastic Volterra equations with singular kernels and Hölder coefficients.
method Established pathwise uniqueness through Hölder continuity of coefficients.
result Pathwise uniqueness and existence of unique strong solutions.
Large deviation principles for multivariate stochastic volatility models.
problem Understanding the behavior of log-processes in multivariate stochastic volatility models.
method Establishing a comprehensive sample path large deviation principle for log-processes.
result Asymptotic formulas for first exit times and barrier option prices derived from the LDP.
On non-negative solutions of stochastic Volterra equations with jumps and non-Lipschitz coefficientsmath.PR
Study on non-negative solutions for stochastic Volterra equations with jumps.
problem Existence and uniqueness of non-negative solutions for stochastic Volterra equations with jumps and non-Lipschitz coefficients.
method Developed a nonnegative approximation approach and used Yamada--Watanabe approximation technique for convergence proof.
result Established conditions for strong existence and pathwise uniqueness of non-negative solutions.
Neural SVEs model complex systems with memory, outperforming traditional methods.
problem Modeling systems with memory effects and irregular behavior.
method Introducing neural stochastic Volterra equations as a physics-inspired architecture.
result Neural SVEs outperform neural SDEs and DeepONets in various applications.
Study approximates rough stochastic volatility models using diffusion processes.
problem High computational cost in simulating rough stochastic volatility models.
method Approximates stochastic Volterra equations with an N-dimensional diffusion process.
result Approximations converge strongly with superpolynomial rate in N.
The study analyzes prediction errors in systems with memory kernels, providing bounds and stability results.
problem Prediction errors in stochastic dynamical systems with memory kernels.
method Analysis of generalized Langevin equations (GLEs) with Volterra equations, integrating synchronized noise coupling and weighted norms.
result Prediction discrepancies decay at a rate determined by the memory kernel's decay, quantitatively bounded by kernel estimation errors.
New theorem handles stochastic Volterra semimartingales.
problem Classic Fubini theorem restrictions for Volterra semimartingales.
method Introduced measure-valued stochastic integration.
result Proved new stochastic Fubini theorem.
Study on fake stationary Volterra Heston model for non-stationary processes.
problem Non-stationary nature of true Volterra equations.
method Weak notion of stationarity (fake stationary regime) for inhomogeneous affine Stochastic Volterra equations.
result Existence of limiting distributions in the long run, which may depend on initial state.
New financial model with sandwiched volatility for option pricing.
problem Developing a new financial model for option pricing.
method Introducing a new model with stochastic volatility driven by a Gaussian Volterra process, ensuring the solution is sandwiched between two arbitrary Hölder continuous functions.
result Developed an algorithm for pricing options with discontinuous payoffs using Malliavin calculus.
New PFPPs based on rank-dependent utility for better performance control.
problem Improving performance prediction in systems with short-term control.
method Introduces rank-dependent PFPPs, solves integral equations via Volterra theory.
result Existence of rank-dependent PFPPs under specific market conditions.
Derives semi-closed form prices for barrier options in the Hull-White model.
problem Calculating prices of barrier options in the Hull-White model with time-dependent parameters.
method Applies generalized integral transform and heat potentials to solve linear Volterra equations of the first kind.
result The method provides more efficient and accurate solutions compared to finite difference methods.
New IBP formulae for rough stochastic Volterra processes.
problem Deriving IBP formulae for path-dependent stochastic Volterra processes.
method Developed a new fractional IBP formula that interpolates between standard and Bismut-Elworthy-Li formulae.
result For rough noise, the expectation is differentiable along constant directions under certain Hölder continuity conditions.
New method for pricing American options in time-dependent models, improving accuracy and efficiency.
problem Pricing American options in time-dependent models with improved accuracy and efficiency.
method Semi-analytical pricing using a nonlinear Volterra integral equation and numerical methods.
result Improved accuracy and efficiency in pricing American options compared to forward finite difference solvers.
Researchers compute Greeks for rough Volterra SV models using Malliavin calculus.
problem Computing Greeks under rough Volterra stochastic volatility models.
method Malliavin calculus techniques, extending integration by parts to non-square integrable functionals.
result Formulas for computing Greeks (Delta, Gamma, Rho, Vega) under various rough Volterra SV models.
Unified approach to stochastic Volterra systems' deviations.
problem Large and moderate deviations for stochastic Volterra systems.
method Weak convergence approach by Budhijara, Dupuis and Ellis.
result Unified treatment of deviations for a broad class of stochastic Volterra equations.
The paper derives formulas for pricing geometric Asian options in the Volterra-Heston model.
problem Pricing geometric Asian options in the Volterra-Heston model.
method Derives semi-closed formulas using Fourier transforms and Riccati-Volterra equations.
result Derives formulas for pricing geometric Asian options with fixed and floating strikes.
In this paper, we study the classical problem of the first passage hitting density of an Ornstein--Uhlenbeck process. We give two complementary (forward and backward) formulations of this problem and provide semi-analytical solutions for both. The corresponding problems are comparable in complexity. By using the method…
New framework analyzes SGD dynamics in large samples and dimensions.
problem Analyzing stochastic gradient descent in large-scale settings.
method Inspired by random matrix theory, new framework for fixed stepsize and finite sum settings.
result SGD dynamics become deterministic in the large sample and dimensional limit, governed by a Volterra integral equation.
We introduce a novel numerical approach for a class of stochastic dynamic programs which arise as discretizations of backward stochastic differential equations or semi-linear partial differential equations. Solving such dynamic programs numerically requires the approximation of nested conditional expectations, i.e., it…
We prove strong existence and uniqueness, and Hölder regularity, of a large class of stochastic Volterra equations, with singular kernels and non-Lipschitz diffusion coefficient. Extending Yamada-Watanabe's theorem, our proof relies on an approximation of the process by a sequence of semimartingales with regularised ke…
New method transforms complex stochastic equations into simpler ones for efficient simulation.
problem Efficient simulation of complex path-dependent stochastic processes.
method Transforms Volterra-type SDEs into standard diffusion processes using convolution kernels.
result Proposes a numerical simulation scheme with a strong convergence rate of 1/2.
Homogenized SGD explains SGD dynamics in high dimensions.
problem Understanding SGD dynamics in high-dimensional settings.
method Developed a homogenized SGD model to analyze high-dimensional SGD.
result Convergent high-dimensional SGD to homogenized SGD for quadratic statistics.
New method for pricing barrier options in time-dependent λ-SABR model.
problem Pricing barrier options in the time-dependent λ-SABR model.
method Modified integral transform method and Fourier-Bessel series solution.
result Semi-analytical solution for barrier options in λ-SABR model.
Model for high-frequency trading with rough volatility.
problem High-frequency trading dynamics and rough volatility modeling.
method Stochastic partial differential equation (SPDE) with rough volatility driven by a Hawkes process.
result The volatility path of the SPDE is rougher than that driven by a standard Brownian motion.
Paper solves stock loan pricing with finite maturity using integral equations.
problem Valuation of margin-call stock loans with finite maturities.
method Fourier Sine transform and Volterra integral equation approach.
result Integral representation of margin-call stock loan value.
Study dynamic asset allocation in incomplete markets using game theory and nonlocal BSDEs.
problem Dynamic mean-variance asset allocation in general incomplete markets with non-exponential discounting.
method Game-theoretic approach, decomposition into myopic and hedging strategies, nonlocal BSDEs, fixed-point theorem.
result Well-posedness of solutions to BSDEs, existence of equilibrium control policy.
New integration method improves BSDE-based PDE solvers.
problem Discretization bias in standard BSDE-based solvers.
method Proposed Stratonovich-based BSDE formulation with stochastic Heun integration.
result Eliminates bias issues and outperforms EM-based variants.
New deep learning method solves complex BSDEs efficiently.
problem Solving high-dimensional nonlinear BSDEs.
method Reformulate as global optimization, approximate solution with deep neural network, globally minimize quadratic local loss functions.
result Demonstrated effectiveness on various high-dimensional nonlinear BSDEs, including finance applications.
Motivated by empirical evidence for rough volatility models, this paper investigates continuous-time mean-variance (MV) portfolio selection under the Volterra Heston model. Due to the non-Markovian and non-semimartingale nature of the model, classic stochastic optimal control frameworks are not directly applicable to t…
Implicit Regularization or Implicit Conditioning? Exact Risk Trajectories of SGD in High Dimensionsstat.ML
SGD outperforms GD in high dimensions via implicit conditioning, revealed by asymptotic analysis.
problem Understanding why SGD outperforms GD in high-dimensional convex problems.
method Asymptotic analysis of multi-pass SGD on high-dimensional convex quadratics, establishing an equivalence to HSGD.
result SGD's efficiency is explained by implicit conditioning, not regularization.
Volterra square-root process boundary behavior and martingale measures
problem Boundary behavior of the Volterra square-root process
method Comparison principles for Volterra integral equations and generalized Riemann-Liouville fractional equations
result Finiteness of negative -moments and atom at the boundary for rough kernels