Estimates drift functions in SDEs using denoising diffusion models.
problem Estimating time-homogeneous drift functions in multivariate SDEs.
method Formulates drift estimation as a denoising problem, trains a conditional diffusion model.
result Proposed estimator matches classical methods in low dimensions and remains competitive in higher dimensions.
The paper tackles drift identification in Lévy α-stable stochastic systems, proposing a Fourier space approach.
problem Estimating the drift field of a stochastic differential equation driven by Lévy α-stable noise.
method Fourier space approach, parameterizing the drift field using Fourier series, minimizing a loss function with gradients computed via the adjoint method.
result The method is capable of learning drift fields in qualitative and/or quantitative agreement with ground truth fields.
Study optimizes financial strategies in markets with uncertain drift.
problem Optimizing portfolios in markets with unpredictable drift.
method Combines worst-case optimization with filtering techniques to define uncertainty sets.
result Proves minimax theorem and derives optimal strategies for continuous updates.
Estimates neural drift for stochastic equations, improving inference on noisy data.
problem Estimating drift in stochastic differential equations with neural networks.
method Non-parametric estimation using ReLU neural networks, enforcing theoretical bounds.
result Practical method for inference on noisy and rough functional data.
New risk bound for drift estimator in stochastic models.
problem Theoretical guarantees for drift estimation in stochastic differential equations.
method Derives an explicit risk bound using diffusion model theory.
result Explicit decomposition of risk into multiple sources of error.
Paper uses sparse learning to estimate quasi-potential and drift components in stochastic systems.
problem Estimating quasi-potential and drift components in stochastic systems.
method Sparse identification of non-linear dynamics (SINDy) combined with action minimization methods.
result Evaluation of quasi-potential landscape from a single trajectory.
Proposes new Monte Carlo methods for calibrating local volatility models with stochastic components.
problem Calibrating local volatility models with stochastic drift and diffusion.
method Developed Monte Carlo algorithms for three models: local volatility with stochastic interest rates, stochastic local volatility with deterministic interest rates, and stochastic local volatility with stochastic interest rates.
result Conditions for the existence of local volatility given European option prices, stochastic interest rate model parameters, and correlations.
New approach to portfolio optimization shows entropy regularization is ineffective.
problem Entropy regularization in mean-variance portfolio optimization under drift uncertainty.
method Combining Bayesian filtering and stochastic policy optimization.
result Entropy regularization does not accelerate learning about unknown drift.
The notion of drift refers to the phenomenon that the distribution, which is underlying the observed data, changes over time. Albeit many attempts were made to deal with drift, formal notions of drift are application-dependent and formulated in various degrees of abstraction and mathematical coherence. In this contribu…
Method learns SDEs from data snapshots.
problem Learning drift and diffusion of SDEs from data.
method Two-step process: learn drift by expected value, learn diffusion by SDP.
result Validated on examples and simulations.
Momentum SGD fails to track nonstationary optima due to drift amplification.
problem Tracking nonstationary optima in stochastic optimization.
method Theoretical analysis of SGD and momentum variants under strong convexity and smoothness.
result Momentum incurs a drift-amplification penalty that diverges as the momentum parameter approaches 1, leading to systematic lag.
We extend Dupire's formula for stochastic interest rates and local volatility.
problem Deriving formulas for stochastic interest rates and local volatility.
method Generalizations of Dupire's formula for stochastic drift and local volatility.
result Validated the limits of the generalized Dupire formulae for specific cases.
Designing deterministic denominators for SGLD stabilizes large drifts.
problem Stabilizing large drifts in SGLD
method Using state-dependent envelopes and empirical quantiles for activation thresholds
result Proxy-quantile denominators are close to oracle-score behavior and improve deterministic taming choices
Improved growth strategies by incorporating stochastic factors in asset returns.
problem Drift uncertainty in asset returns makes growth optimization strategies sensitive.
method Study robust growth-optimization in high-dimensional incomplete markets under drift uncertainty and ergodicity.
result Utilizing stochastic factors improves robust growth rates and optimal strategies.
We consider an optimal investment and consumption problem for a Black-Scholes financial market with stochastic volatility and unknown stock appreciation rate. The volatility parameter is driven by an external economic factor modeled as a diffusion process of Ornstein-Uhlenbeck type with unknown drift. We use the dynami…
Proposes a method to estimate SDE noise from a single trajectory.
problem Estimating SDE noise from a single data trajectory without ergodicity or stationarity.
method Combining Taylor expansions, Girsanov transformations, and drift function's initial value for drift and noise estimation.
result First SSISDE algorithm capable of identifying SDE dynamics from a single trajectory.
Optimal liquidation of an asset with unknown constant drift and stochastic regime-switching volatility is studied. The uncertainty about the drift is represented by an arbitrary probability distribution; the stochastic volatility is modelled by m-state Markov chain. Using filtering theory, an equivalent reformulation…
Unified geometric framework for Brownian motion on various manifolds.
problem Modeling Brownian motion on complex Riemannian manifolds.
method Constructing stochastic differential equations with noise and drift terms aligned with Laplace-Beltrami operators.
result Geometrically transparent and mathematically consistent foundation for diffusion processes.
Proposes a virtual bidding strategy for electricity markets using stochastic control.
problem Optimizing electricity prices in day-ahead and real-time markets.
method Modeling price differences as Brownian motion with meteorological variables, transforming into portfolio management problem.
result Developed a strategy to manage electricity prices efficiently.
In the present paper, an expansion of the transition density of Hyperbolic Brownian motion with drift is given, which is potentially useful for pricing and hedging of options under stochastic volatility models. We work on a condition on the drift which dramatically simplifies the proof.
We apply results of Malliavin-Thalmaier-Watanabe for strong and weak Taylor expansions of solutions of perturbed stochastic differential equations (SDEs). In particular, we work out weight expressions for the Taylor coefficients of the expansion. The results are applied to LIBOR market models in order to deal with the …
The paper optimizes interpolation schedules in generative models to improve sampling accuracy.
problem Improving sampling accuracy in generative models with fewer resources.
method Minimizing the averaged squared Lipschitzness of the drift field, using transfer formulas.
result Designed schedules yield more accurate fine-scale statistics at fixed integrator budget.
Optimal investment strategy with expert opinions in uncertain conditions.
problem Optimizing wealth in a model with unobservable drift and costly expert opinions.
method Embedding into a full information problem, using viscosity solutions and stochastic Perron's method.
result Constructing optimal trading and expert opinion strategies under sufficient regularity conditions.
A new method estimates SDEs using occupation kernels.
problem Learning multivariate stochastic differential equations (SDEs).
method Two-step procedure: estimate drift, then diffusion. Occupation kernels used in RKHS.
result Validated on simulated and real-world data.
Study explains mortgage burnout using Cox hazard models.
problem Understanding burnout in mortgage pools.
method Modeling mortgage prepayment using Cox hazard processes.
result Observed pool hazard is a survival-weighted mean of individual hazards with a selection term.
The maximum likelihood approach is adapted to the problem of estimation of drift and diffusion functions of stochastic processes from measured time series. We reconcile a previously devised iterative procedure [Kleinhans et al., Physics Letters A (346), 2005] and put the application of the method on a firm theoretical …
Statistic dynamics of financial systems is investigated, basing on a model of randomly coupled equation system driven by stochastic Langevin force. It is found that in stable regime the noise power spectrum of the system is of 1/f^alpha form, with the exponent alpha=3/2 in case of Hermitian coupling matrices, or slight…
This paper presents a novel one-factor stochastic volatility model where the instantaneous volatility of the asset log-return is a diffusion with a quadratic drift and a linear dispersion function. The instantaneous volatility mean reverts around a constant level, with a speed of mean reversion that is affine in the in…
The paper analyzes convergence rates for stochastic approximation and reinforcement learning.
problem Establishing almost sure convergence rates for stochastic approximation and reinforcement learning under Markovian noise.
method A novel Lyapunov drift construction that applies a Poisson-equation based correction for Markovian noise to the Moreau-envelope smoothing for contractive mappings.
result Almost sure convergence rates for specific learning rates are derived, with rates arbitrarily close to o(n1−2η) and o(n−1). Algorithm learns stochastic system dynamics from data.
problem Recovering interpretable symbolic expressions for stochastic systems.
method Data-driven, trajectory averaging, drift-informed correction.
result Recover coefficients and densities to within 5% and 0.01 in total variation, respectively.
Study builds a classifier for diffusions with unknown diffusion but known drifts.
problem Multiclass classification of S.D.E. paths with unknown diffusion coefficient.
method Plug-in classifier using nonparametric estimators of drift and diffusion functions.
result Consistent classification procedure with rate of convergence under different assumptions.
This paper extends neural network approximation results to denoising diffusion models.
problem Improving the efficiency and accuracy of generative models.
method Leveraging connections to stochastic control and neural network approximation.
result Established neural network approximation results for the Föllmer drift are extended to denoising diffusion models.
We reformulate wealth taxation using Fokker-Planck equations to ensure tax neutrality.
problem Ensuring tax neutrality in wealth taxation frameworks.
method Reformulating the neutral wealth tax framework using stochastic dynamics and statistical physics, specifically Fokker-Planck equations.
result The framework clarifies when wealth taxation is a benign rescaling of dynamics and when it introduces new physics.
Algorithm minimizes risk for multiclass classification of stochastic diffusion paths.
problem Multiclass classification of stochastic diffusion paths with distinct drift functions.
method Empirical risk minimization using L2 risk.
result Achieves fast rates of convergence under margin assumption.
We introduce a nonparametric approach for estimating drift and diffusion functions in systems of stochastic differential equations from observations of the state vector. Gaussian processes are used as flexible models for these functions and estimates are calculated directly from dense data sets using Gaussian process r…
Unified framework for Brownian motion distances on specific geometric manifolds.
problem Understanding Brownian motion distances on radially isoparametric manifolds.
method Developed a geometric framework and derived drift-window inequalities.
result Unified framework for coadapted Brownian couplings on RIM.
This paper aims to make a new contribution to the study of lifetime ruin problem by considering investment in two hedge funds with high-watermark fees and drift uncertainty. Due to multi-dimensional performance fees that are charged whenever each fund profit exceeds its historical maximum, the value function is expecte…
Generative model for hypergraphs captures complex interactions without pairwise reductions.
problem Challenges in generating realistic hypergraphs with pairwise reductions.
method Structured stochastic diffusion on relaxed incidence matrices.
result Generative model preserves structure-aware noising and yields explicit Gaussian law.
Paper proves convergence of Markovian iteration for FBSDEs with fully coupled drift and Z process.
problem Proving convergence of Markovian iteration for FBSDEs with fully coupled drift and Z process.
method Differentiation-based approach to handle Z process, uniformly controlling Lipschitz continuity of decoupling fields.
result Proves convergence of Markovian iteration method for FBSDEs with fully coupled drift and Z process.
In this paper, we study the mean-variance portfolio selection problem under partial information with drift uncertainty. First we show that the market model is complete even in this case while the information is not complete and the drift is uncertain. Then, the optimal strategy based on partial information is derived, …
We give a complete solution to the problem of minimizing the expected liquidity costs in presence of a general drift when the underlying market impact model has linear transient price impact with exponential resilience. It turns out that this problem is well-posed only if the drift is absolutely continuous. Optimal str…
We discuss martingales, detrending data, and the efficient market hypothesis for stochastic processes x(t) with arbitrary diffusion coefficients D(x,t). Beginning with x-independent drift coefficients R(t) we show that Martingale stochastic processes generate uncorrelated, generally nonstationary increments. Generally,…
CSI method learns conditional distributions by estimating flow equations.
problem Learning conditional distributions in generative models.
method Estimates probability flow equations to transport reference to target distribution.
result Derives explicit expressions for conditional drift and score functions.
Unified framework for generating synthetic financial time series that accurately capture both marginal distributions and temporal dynamics.
problem Generating synthetic financial time series that reproduce both marginal distributions and temporal dynamics.
method SBBTS: A unified Schrödinger-Bass framework for synthetic financial time series.
result SBBTS accurately recovers stochastic volatility and correlation parameters that prior methods fail to capture.
The paper develops a method to learn SDE drift functions from sparse, noisy data.
problem Learning SDE drift functions from sparse and noisy data without strong structural assumptions.
method Data-driven approach using a penalized negative log-likelihood functional over RKHS, with an EM algorithm employing SMC for approximations.
result The method enables accurate estimation of SDE drift functions in low-data regimes.
New method identifies SDE drift and diffusion from temporal data.
problem Learning SDE parameters from temporal data, especially in noisy or incomplete data.
method Entropy-regularized optimal transport, APPEX algorithm.
result Can almost always recover drift and diffusion from temporal marginals.
ESPD improves learning efficiency in sparse reward reinforcement learning.
problem Sparse reward reinforcement learning challenges.
method Evolutionary Stochastic Policy Distillation (ESPD) based on drifted random walk insight.
result High learning efficiency demonstrated in MuJoCo robotics control suite experiments.
Consider the problem of learning the drift coefficient of a stochastic differential equation from a sample path. In this paper, we assume that the drift is parametrized by a high dimensional vector. We address the question of how long the system needs to be observed in order to learn this vector of parameters. We prove…