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arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

168,657 papers · 148 categories

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2715438141,085 · Jun 202019922001200920172026
48 results for stochastic path problems

New control theory for self-path-dependent problems solves unique constraints.

problem Optimal control with self-path-dependent constraints in stochastic systems.
method Introduces new HJB equations for variational inequalities with historical maximum controls.
result Value functions are viscosity solutions to HJB equations under Lipschitz conditions.

Unified approach to stochastic control, filtering, and stopping using rough paths.

problem Addressing gaps in classical problems of stochastic control, filtering, and stopping.
method Combining rough path theory with controlled rough paths to provide a pathwise deterministic framework.
result Established rigorous connection between candidate solutions and Hamilton-Jacobi-Bellman equation.

The paper identifies network bottlenecks using minimax paths in stochastic networks.

problem Identifying bottlenecks in networks with stochastic weights.
method Modeling as combinatorial semi-bandit problem, applying combinatorial Thompson Sampling, and approximating the original objective due to computational intractability.
result Established an upper bound on Bayesian regret and evaluated Thompson Sampling performance on real-world networks.

The paper provides an efficient method to price path-dependent derivatives using multiscale stochastic volatility models.

problem Pricing path-dependent derivatives under multiscale stochastic volatility models.
method Derives a Malliavin representation for the first-order approximation of the price of path-dependent derivatives.
result An efficient Monte Carlo approximation for pricing path-dependent derivatives is derived.

The paper solves optimal control problems for stochastic delay equations.

problem Optimal control of stochastic delay differential equations.
method Rewriting the problem in an infinite-dimensional Hilbert space, using dynamic programming and viscosity solutions.
result Characterizes the value function as the unique viscosity solution of the Hamilton-Jacobi-Bellman equation.

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.

Paper introduces a new volatility model for natural gas markets and discusses swing option pricing.

problem Modeling price and storage dynamics in natural gas markets with path-dependent volatility.
method Developed a novel stochastic path-dependent volatility model and used deep learning for swing option pricing.
result Proposed a deep learning method for numerical approximations of swing option pricing.

Paper proposes method for generating paths of stochastic volatility CGMY process for option pricing.

problem Generating accurate sample paths for stochastic volatility models for option pricing.
method Monte-Carlo method for European and American options, least square regression for calibration.
result Calibrated model parameters to S\&P 100 index options market using path-dependent options.

Proposes a new method to learn entire solution paths without discretization.

problem Optimizing a family of problems indexed by hyperparameters.
method Parameterizes the solution path with basis functions and solves a single stochastic optimization problem.
result Uniform error of learned path converges linearly to a constant related to basis expressiveness.

Investment strategies in occupational pension plans are optimized for non-tradable income risk.

problem Optimizing investment strategies for occupational pension plans in the presence of non-tradable income risk.
method Formulated as a stochastic optimization problem, analyzed in both constant and stochastic volatility environments.
result Random contributions induce the optimal glide path structure, influenced by initial wealth, contributions, and risk aversion.

The path probability of a particle undergoing stochastic motion is studied by the use of functional technique, and the general formula is derived for the path probability distribution functional. The probability of finding paths inside a tube/band, the center of which is stipulated by a given path, is analytically eval…

2016-02-13abs ↗pdf ↗

Quantum computing speeds up analysis of financial stochastic processes.

problem Challenging simulation and analysis of continuous time stochastic processes.
method Established a quantum framework for efficient state preparation and information extraction.
result Extraction of path-dependent and history-sensitive information from stochastic processes efficiently.

Develops a machine learning framework for computing most probable paths in stochastic systems.

problem Computing the most probable paths in stochastic dynamical systems.
method Reformulates the boundary value problem of Hamiltonian systems and uses a neural network to solve the Euler-Lagrange equation for the Onsager-Machlup action functional.
result Demonstrates the efficacy and accuracy of the machine learning approach in computing most probable paths for stochastic systems with various types of noise.

The paper develops a deep signature approach for option pricing under non-Markovian stochastic volatility models.

problem Pricing options under non-Markovian stochastic volatility models is challenging due to the dependence on historical paths.
method Reformulate the asset dynamics as a rough stochastic differential equation and represent rough paths via signatures. Apply standard analytical tools to solve the transformed equation.
result The deep signature approach provides a theoretically grounded and computationally efficient framework for option pricing.

Reduces path integrals for interacting systems using dependent coordinates.

problem Reducing path integrals for systems with symmetry.
method Reduction procedure based on Wiener-type path integral, optimal nonlinear filtering, and projection of mean curvature vector field.
result Shows non-invariance of the measure in the path integral under reduction and generates the Jacobian.

This paper considers possible price paths of a financial security in an idealized market. Its main result is that the variation index of typical price paths is at most 2, in this sense, typical price paths are not rougher than typical paths of Brownian motion. We do not make any stochastic assumptions and only assume t…

2010-05-03abs ↗pdf ↗

Stochastic version of alternating direction method of multiplier (ADMM) and its variants (linearized ADMM, gradient-based ADMM) plays a key role for modern large scale machine learning problems. One example is the regularized empirical risk minimization problem. In this work, we put different variants of stochastic ADM…

2020-03-07abs ↗pdf ↗

Deep neural networks solve stochastic control problems with delay.

problem Challenges in stochastic control problems with delay due to path-dependence and high dimensions.
method Employing recurrent neural networks (RNNs) to parameterize policies and optimize objectives.
result RNNs, especially LSTMs, efficiently capture path-dependence and outperform feedforward networks in training and performance.

This paper studies a class of non-Markovian singular stochastic control problems, for which we provide a novel probabilistic representation. The solution of such control problem is proved to identify with the solution of a ZZ-constrained BSDE, with dynamics associated to a non singular underlying forward process. Du…

2017-01-30abs ↗pdf ↗

Universal approximation for stochastic processes using Brownian motion.

problem Approximating stochastic processes with linear functionals.
method Establishing LpL^p-type universal approximation theorems for rough path spaces.
result Linear functionals on the signature of time-extended Brownian motion can approximate any pp-integrable stochastic process.

The paper proves signatures of non-geometric rough paths can approximate functionals uniformly.

problem Approximating functionals of non-geometric rough paths.
method Extending rough paths with time and quadratic variation terms, proving uniform approximation.
result Linear functionals of extended signatures uniformly approximate continuous functionals.

This paper optimizes dividend payout rates with a drawdown constraint in a stochastic model.

problem Optimizing dividend payout rates while avoiding drawdowns in a stochastic model.
method Solving a path-dependent stochastic control problem using Hamilton-Jacobi-Bellman equations and PDE methods.
result Explicit characterization of an optimal feedback control strategy, including two free boundaries and the running maximum surplus process.

The dual representation of the martingale optimal transport problem in the Skorokhod space of multi dimensional cadlag processes is proved. The dual is a minimization problem with constraints involving stochastic integrals and is similar to the Kantorovich dual of the standard optimal transport problem. The constraints…

2014-04-05abs ↗pdf ↗

Efficient hybrid method for pricing barrier options with stochastic volatility.

problem Valuation of barrier options on assets with stochastic volatility.
method Combining Monte Carlo simulation and semi-analytical heat potential method.
result Our method provides better accuracy and is orders of magnitude faster than existing methods.

Unified approach to DP problems using Gumbel distribution and variational Bayesian inference.

problem Solving classical optimal path problems in a probabilistic framework.
method Gumbel distribution and variational Bayesian inference for latent optimal paths.
result Unified approach transforms DP problems into directed acyclic graphs with Gibbs distribution.

Path signatures reveal community structure in coupled oscillators' dynamics.

problem Detecting communities in multivariate dynamical processes from time series data.
method Path signatures, a mathematical framework encoding geometric and temporal properties of continuous paths.
result Achieved exact recovery of structural communities from observed time series in multiple KSBM instances.

Novel framework synthesizes stochastic trajectories with anticipated structural breaks.

problem Synthesizing forward-looking, time-evolving stochastic trajectories with anticipated structural breaks.
method Anticipatory Neural Jump-Diffusion (ANJD) flow, AVNSG for dynamic spectral whitening.
result The framework effectively captures non-commutative moments and high-order stochastic texture.

Study online learning in MDPs with aggregate bandit feedback, achieving low regret in both stochastic and adversarial settings.

problem Online learning in finite-horizon episodic MDPs with aggregate bandit feedback.
method Best-of-both-worlds (BOBW) algorithms using FTRL over occupancy measures, self-bounding techniques, and new loss estimators.
result First BOBW algorithms for episodic tabular MDPs with aggregate bandit feedback achieving O(logT)O(\log T) regret in stochastic and O(T){O}(\sqrt{T}) regret in adversarial settings.

Foundation for robust finance using rough path theory.

problem Mathematical models of financial markets under Knightian uncertainty.
method Introducing Property (RIE) for càdlàg paths, proving existence of rough integrals, verifying admissibility of trading strategies.
result Existence and stability of rough path integrals for non-gradient integrands.

Study shows hard sample complexity for learning optimal policies in stochastic shortest path problems.

problem Learning optimal policies in stochastic shortest path problems.
method Analyzes sample complexity with and without generative models, derives lower and upper bounds.
result Proves sample complexity bounds and impossibility of horizon-free regret in SSPs.

We use GANs and signatures to approximate conditional laws in filtering and prediction of diffusion processes.

problem Approximating conditional laws for diffusion processes with noisy observations.
method Conditional GANs combined with signatures for approximation.
result Efficient approximation of conditional laws for diffusion processes.