The study examines hedging strategies in financial models with transaction costs.
problem Hedging strategies under transaction costs in financial models.
method Analysis of Gaussian Volterra processes and conditional-mean hedging.
result Derivation of a formula for prediction laws in Gaussian Volterra processes.
Study predicts Gaussian Volterra processes with noisy Brownian motion.
problem Predicting Gaussian Volterra processes with hidden Brownian motion.
method Regular conditional law analysis under model disturbances.
result Developed method for variance reduction in measurement errors.
Study large deviation principle for fractional stochastic volatility models.
problem Large deviation principle for Volterra type fractional stochastic volatility models.
method Prove a small-noise large deviation principle under weaker conditions.
result Derive large deviation principle in small-time regime.
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.
The paper introduces a method for learning nonparametric Volterra kernels using Gaussian processes.
problem Learning nonparametric nonlinear operators from data.
method NVKM model using Volterra series and Gaussian processes for unobserved and observed input functions.
result The NVKM model can perform both single and multiple output regression and system identification.
Study volatility models with rough paths, focusing on large deviations and option behavior.
problem Analyzing volatility in financial markets with very rough paths.
method Introduced time-inhomogeneous stochastic volatility models with Volterra Gaussian processes.
result Obtained large deviation principles for log-price processes in super rough Gaussian models.
Paper introduces non-linear process convolutions for multi-output Gaussian processes.
problem Building accurate covariance functions for multi-output Gaussian processes.
method Volterra series for non-linearity, closed-form expressions for mean and covariance.
result Non-linear model outperforms classical process convolution in synthetic and real datasets.
The paper introduces new processes for modeling multivariate volatility.
problem Developing new stochastic processes for multivariate volatility modeling.
method Introducing Volterra Wishart and Volterra pure jump processes with fractional kernels.
result Affine covariance processes for multivariate volatility modeling.
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.
Study develops methods for pricing and hedging volatility options in rough volatility models.
problem Pricing and hedging volatility options in rough volatility models, especially for VIX products.
method Developed efficient Monte Carlo methods and asymptotic approximations for Gaussian Volterra process models, and introduced modulated Volterra processes for VIX smile.
result Modulated Volterra processes successfully capture the VIX smile, improving model fit for VIX products.
Defines a new short rate model and convexity adjustment formulae.
problem Interest rate convexity in a Gaussian framework.
method Defines a short rate model driven by a Gaussian Volterra process and derives convexity adjustment formulae.
result Explicit formulae for convexity adjustment derived.
Researchers derive an explicit Laplace transform for integrated Volterra Wishart process.
problem Modeling and pricing financial instruments with complex covariance structures.
method Explicit expression for conditional Laplace transform of integrated Volterra Wishart process, linking to matrix Riccati equations.
result Derivation of Laplace transform for a special case of convolution kernel, leading to efficient pricing methods.
Path-dependent PDEs model VIX and Realised Variance options.
problem Modeling volatility derivatives with path-dependence.
method Continuous stochastic volatility model with Gaussian Volterra process, proving well-posedness of PDEs.
result Formulae for greeks and implied volatility provided, finite-dimensional pricing PDEs obtained in Markovian models.
The Volterra square-root process shows non-uniqueness of limiting distributions and regularity of its law.
problem Non-uniqueness of limiting distributions in the Volterra square-root process.
method Establishing existence of limiting distributions using integrability of the Volterra convolution kernel and exponential-affine transformation.
result The limiting distributions of the Volterra square-root process depend on the initial state and belong to weighted Besov spaces.
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.
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.
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.
State spaces of multifactor approximations of nonnegative Volterra processes are linear transformations of the nonnegative orthant.
problem Characterizing state spaces of multifactor approximations of nonnegative Volterra processes.
method Explicit linear transformation of the nonnegative orthant.
result State spaces of multifactor approximations of nonnegative Volterra processes are given by explicit linear transformation of the nonnegative orthant.
Researchers find the optimal exercise time for American options using a specific type of diffusion process.
problem Finding the optimal time to exercise American options with a time-dependent Ornstein-Uhlenbeck process.
method Optimal stopping problem, probabilistic arguments, non-linear Volterra-type integral equation, Picard iteration algorithm.
result They derive a non-linear Volterra-type integral equation and prove the exercise boundary's Lipschitz continuity and differentiability almost everywhere.
Paper offers a new method for pricing financial derivatives under rough stochastic volatility models.
problem Challenges in pricing financial derivatives, especially vanilla options, for rough stochastic volatility models.
method Developed a decomposition formula and prediction law for European option pricing under general Gaussian Volterra processes.
result Explicit semi-closed approximation formula for rough fractional volatility models, significantly improving computational efficiency.
Study on Volterra Cox-Ingersoll-Ross process, proving asymptotic independence and ergodicity.
problem Analyzing the Volterra Cox-Ingersoll-Ross process and its properties.
method Fine asymptotic analysis of Volterra Riccati equation, affine transformation formula.
result Proves asymptotic independence and ergodicity of the process.
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 p-moments and atom at the boundary for rough kernels 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.
We propose a finite difference scheme to simulate solutions to a certain type of hyperbolic stochastic partial differential equation (HSPDE). These solutions can in turn estimate so called volatility modulated Volterra (VMV) processes and Lévy semistationary (LSS) processes, which is a class of processes that have been…
Study proves existence, uniqueness, and stability for specific stochastic Volterra equations.
problem Analyzing existence, uniqueness, and stability of affine stochastic Volterra equations with L1-kernels. method Approximations with L2-kernels, stability result, duality argument, deterministic Riccati--Volterra integral equation. result Established weak uniqueness for the equations using Fourier--Laplace transform and a deterministic Riccati--Volterra integral equation.
We simplify Volterra process predictions by reducing dimensionality and using a tailored deep learning model.
problem Predicting the conditional law of Volterra processes with stochastic volatility is challenging due to high dimensionality and non-smoothness.
method We developed a stable dimension reduction technique onto a low-dimensional statistical manifold of non-positive curvature and introduced a sequentially deep learning model tailored to this geometry.
result Our model can approximate the conditional law of Volterra processes with approximation rates achievable only with very large networks.
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 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 paper studies Hawkes processes under mean-field limits and criticality conditions.
problem Analyzing nearly unstable Hawkes processes in a mean-field regime.
method Extending the method by Jaisson and Rosenbaum, establishing scaling limits and propagation of chaos.
result Scaling limits of Hawkes processes are stochastic Volterra diffusions of affine type, with three distinct limiting regimes.
Unified model for financial derivatives pricing with stochastic interest rates.
problem Pricing and hedging financial derivatives with stochastic interest rates.
method Volterra Stein-Stein model with correlated Gaussian Volterra processes.
result Explicit formulas for bond and cap/floor pricing, and characteristic function for log-forward index.
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.
The study improves volatility model pricing accuracy with new statistical expansions.
problem Improving option pricing accuracy in volatility models.
method Developed Edgeworth expansions for various volatility models.
result Enhanced statistical expansions for volatility models.
Investigates Merton's portfolio problem in a rough stochastic environment with Volterra Heston model.
problem Optimizing investment strategies in a non-Markovian, non-semimartingale stochastic environment.
method Solves the portfolio optimization problem using the martingale optimality principle and auxiliary random process.
result Derives semi-closed form solutions for optimal strategies under power and exponential utilities.
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.
Fast simulates Volterra processes using RFF, focusing on S-fBM.
problem Efficiently simulate Volterra processes for fractional Brownian motion.
method Random Fourier Features (RFF) approximation of kernel, spectral representation, Hamiltonian Monte Carlo sampling.
result Quantitative guarantees for RFF approximation, competitive in terms of efficiency and error.
Investigates portfolio selection under rough volatility model, showing quadratic efficient frontier.
problem Mean-variance portfolio selection under rough volatility models.
method Constructs an auxiliary stochastic process to solve Riccati-Volterra equation for optimal strategy.
result MV efficient frontier is quadratic, influenced by roughness and volatility of volatility.
Investor optimizes investment timing with future knowledge, overcoming transaction costs.
problem Optimal investment timing with future peeking, constrained by transaction costs.
method Solves control problem with infinite-dimensional memory using Gaussian Volterra integral equations.
result Explicit solution to optimal investment problem in Bachelier setting.
Paper proves SVV model reproduces power-law skew in implied volatilities.
problem Reproducing power-law behavior in implied volatility skew.
method Analytical proof using Malliavin calculus and Volterra kernel selection.
result SVV model reproduces power-law skew under correct kernel choice.
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 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.
New algorithms compute Volterra signature efficiently for time series analysis.
problem Efficient computation of Volterra signature with matrix-valued kernels.
method Decomposed Chen-type convolution relation, introduced FFT-based and exact recursion algorithms.
result Efficient algorithms for Volterra signature computation with various complexities.
We derive the price of a spread option based on two assets which follow a bivariate volatility modulated Volterra process dynamics. Such a price dynamics is particularly relevant in energy markets, modelling for example the spot price of power and gas. Volatility modulated Volterra processes are in general not semimart…
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 measures inequality in social-economic systems using Fokker-Planck equations and Lotka-Volterra dynamics.
problem Measuring inequality in oscillatory social-economic systems described by Fokker-Planck equations and Lotka-Volterra dynamics.
method Used Fokker-Planck equations and Lotka-Volterra dynamics to model inequality, focusing on coefficient of variation as a measure.
result Inequality initially tends to decrease in oscillatory systems, contrary to steady-state models.
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.
The paper analyzes time-inconsistent strategies in financial markets with rough volatility.
problem Time-inconsistency in financial markets with rough volatility.
method Functional Itô calculus and game-theoretic framework to solve path-dependent Hamilton-Jacobi-Bellman equations.
result Explicit solutions to MVP problems under rough volatility, showing performance benefits.
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.
No-arbitrage leads to power-law market impact and rough volatility.
problem Understanding market impact and volatility dynamics.
method Mathematical proof and analysis of stochastic Volterra equations.
result Market impact function is power-law, implying rough volatility.