The paper analyzes time-dependent streaming data with biased gradient estimates and proposes improved stochastic optimization methods.
problem Stochastic optimization in a streaming setting with time-dependent and biased gradient estimates.
method Analysis of several first-order methods including SGD, mini-batch SGD, and time-varying mini-batch SGD, along with their Polyak-Ruppert averages.
result Time-varying mini-batch SGD methods can break long- and short-range dependence structures, and biased SGD methods can achieve comparable performance to their unbiased counterparts.
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.
Paper introduces CIM for detecting dependence and monotonicity between stochastic signals.
problem Detecting the strength and monotonicity structure of dependence between stochastic signals.
method Nonparametric copula-based index (CIM) that satisfies desirable properties of measures of association.
result CIM shows favorable performance in detecting monotonicity and dependence in real-world data.
Improved simulation for path-dependent options without matrix inversion.
problem Evaluating path-dependent options efficiently and accurately.
method Stochastic approximation, explicit solutions to Heston model, importance sampling.
result Up to two orders of magnitude speed improvement over standard Monte Carlo methods.
Improved convergence for nonconvex optimization with dependent data.
problem Constrained smooth nonconvex optimization with dependent data.
method Stochastic projected gradient methods under a general dependent data sampling scheme.
result Achieved worst-case rate of convergence ildeO(t−1/4) and complexity ildeO(ε−4). Proposes logistic-beta process for modeling dependent probabilities with beta marginals.
problem Limited work on flexible and computationally convenient stochastic process extensions for dependent random probabilities.
method Introduces logistic-beta process with logistic transformation and beta marginals, capable of modeling dependence in discrete and continuous domains.
result Logistic-beta processes enable effective posterior inference and design of computationally tractable dependent Bayesian nonparametric models.
New tail dependence measures for stock indices.
problem Measuring tail dependence between financial variables.
method Introducing a new stochastic order and studying monotone tail dependence measures.
result Advantage of new tail dependence measures over classical ones.
Pricing bonus certificates and barrier products uses efficient interpolation and stochastic modeling.
problem Pricing bonus certificates and barrier products with American conditions.
method Efficient interpolation for European conditions, stochastic modeling for American conditions.
result Pricing can be done without stochastic modeling within a certain accuracy range.
New algorithm optimizes multi-armed bandit performance in stochastic and adversarial settings.
problem Optimizing multi-armed bandit performance in both stochastic and adversarial environments.
method Follow-the-regularized-leader method with adaptive learning rates.
result First BOBW algorithm with gap-variance-dependent regret bounds in adversarial settings.
Study efficient algorithms for nonconvex optimization with state-dependent Markov data.
problem Stochastic optimization with Markovian data and state-dependent transition kernels.
method Projection-based and projection-free algorithms for constrained nonconvex problems.
result The number of oracle calls to achieve an ε-stationary point is O(1/ε2.5). New analysis for sampling from non-convex distributions with dependent data.
problem Sampling from non-logconcave distributions in stochastic optimization.
method Stochastic Gradient Langevin Dynamics (SGLD) with dependent data streams.
result Sharper and uniform convergence estimates in L1-Wasserstein distance. 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.
This work extends variance reduction for path-dependent derivatives to affine stochastic volatility models.
problem Pricing path-dependent derivatives in affine stochastic volatility models.
method Prove large deviations principle, apply Esscher transform, use Varadhan's lemma.
result Numerical efficiency demonstrated on Heston model with and without jumps.
GMMNs model cross-sectional dependence for better option pricing and simulation.
problem Modeling cross-sectional dependence between stochastic processes.
method Generative moment matching networks (GMMNs) for geometric Brownian motions and ARMA-GARCH models.
result GMMNs produce dependent quasi-random samples with variance reduction.
New bounds on random quadratic forms hold under dependence, useful for adaptive modeling.
problem Need for independence in bounds on random quadratic forms.
method Uniform bounds on random quadratic forms of conditionally independent and sub-Gaussian stochastic processes.
result Bounds hold under general dependencies and sequential design.
Linking SV and PDV models for better volatility forecasts.
problem Improving volatility forecasting models.
method Assumed density filtering to map SV models to PDV representations, introducing calibration procedure.
result Improves in-sample fit and robust out-of-sample forecasts.
The paper tackles robust control with uncertain dependence using data-driven methods.
problem Nonparametric robust control under dependence uncertainty in multi-period stochastic systems.
method Nonparametric adaptive robust control framework using stochastic gradient descent ascent algorithm.
result The controller benefits from knowing more about the uncertain model.
The paper extends first-order asymptotics for path-dependent derivatives in multiscale stochastic volatility.
problem Analyzing path-dependent derivatives in a multiscale stochastic volatility environment.
method First-order asymptotics analysis using Dupire's functional Ito calculus.
result Market parameters calibrated to vanilla options can price path-dependent derivatives to the same order.
STCN combines TCNs with stochastic latent variables for sequence modeling.
problem Performance gap between TCNs and stochastic RNNs, especially with multiple layers of random variables.
method Proposes a hierarchy of stochastic latent variables in a modular architecture.
result Achieves state-of-the-art log-likelihoods across various tasks.
Unexpectedly, weighted Pareto variables are stochastically dominant.
problem Understanding stochastic dominance in Pareto distributions.
method Analyzing weighted averages of Pareto random variables with infinite mean.
result The weighted average of Pareto variables is stochastically dominant.
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.
Stochastic algo learns from evolving data, achieving optimal performance.
problem Performative prediction and multiplayer extensions.
method Stochastic approximation with decision-dependent distributions.
result Asymptotic normality and optimality of the algorithm's performance.
Proposes a method to estimate time-dependent probability density functions using binary classifiers.
problem Estimating time-dependent probability density functions of stochastic processes.
method Trains a time-dependent binary classifier to discriminate between realizations of a stochastic process at two nearby time instants.
result Explicitly models and accurately reconstructs complex time-dependent, multi-modal, and near-degenerate densities.
New algorithm tackles stochastic bandits with varying arm-dependent delays.
problem Applying existing algorithms to stochastic delayed bandit settings is restricted by strong assumptions on delay distributions.
method Proposes a simple UCB-based algorithm called PatientBandits that weakens assumptions on delay distributions.
result Provides bounds on regret and performance lower bounds for the PatientBandits algorithm.
SNP extends Neural Processes to handle temporal dependencies in sequences.
problem Handling temporal dependencies in sequences of stochastic processes.
method Integrates a temporal state-transition model into Neural Processes.
result First 4D model capable of dynamic 3D scene modeling.
Study on pairwise counter-monotonicity, a type of negative dependence.
problem Understanding and quantifying extremal negative dependence structures.
method Established stochastic representation and invariance property; showed implications and connections.
result Pairwise counter-monotonicity implies negative association and joint mix dependence.
In this paper new analytical and numerical approaches to valuating path-dependent options of European type have been developed. The model of stochastic volatility as a basic model has been chosen. For European options we could improve the path integral method, proposed B. Baaquie, and generalized it to the case of path…
New SGMCMC method controls bias in SSMs for long time series.
problem Inference in SSMs is computationally prohibitive for long time series.
method Proposed new stochastic gradient estimators to control bias in SSMs.
result Developed novel SGMCMC samplers for various SSM types.
New algorithms reduce regret in online MDPs by adapting to data and variance.
problem Adapting to both adversarial and stochastic environments in online MDPs.
method Develops algorithms based on global optimization and policy optimization, using optimistic follow-the-regularized-leader with log-barrier regularization.
result Achieves refined data-dependent and variance-dependent regret bounds.
New formulas for pricing Asian and basket options using stochastic expansion.
problem Pricing Asian and basket options under time-dependent parameters.
method Stochastic Taylor expansion around a log-normal proxy model.
result Highly accurate approximations for Asian options and vanilla options with discrete dividends.
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.
Temporal Normalizing Flows enhance density estimation of time-dependent data.
problem Accurate and robust density estimation of time-dependent stochastic data.
method Leveraging normalizing flows for temporal data, tNFs estimate multi-scale distributions without prior scale knowledge.
result Temporal Normalizing Flows improve density estimation of time-dependent data, including multi-scale distributions.
The paper analyzes Euler approximations for complex volatility models with strong convergence rates.
problem Analyzing strong convergence rates for Euler approximations in stochastic path-dependent volatility models.
method Proposes a Monte Carlo simulation scheme combining log-Euler and truncation/Euler-Maruyama schemes.
result Establishes strong convergence rate of 1/2 for the approximation process up to a critical time.
Study sampling from logconcave distributions with dependent data streams.
problem Sampling from logconcave distributions with biased gradient estimates.
method Euler discretization of Langevin SDEs with dependent data.
result Upper bound on Wasserstein-2 distance between iterates and target distribution.
Training-free model learns SDE dynamics without training, accelerating parameter studies.
problem High computational cost of simulating parameter-dependent SDEs.
method Training-free conditional diffusion model with joint kernel-weighted Monte Carlo estimator.
result Accurate approximation of conditional distributions across varying parameter values.
New algorithm optimizes stochastic optimization with circular dependency.
problem Circular dependency between decision variable and importance sampling.
method Single-loop stochastic approximation algorithm based on Nesterov's dual averaging.
result Achieves minimal asymptotic variance and resolves circular optimization challenge.
Study on SA with heavy-tailed and LRD noise, establishing finite-time bounds.
problem Analyzing stochastic approximation under heavy-tailed and LRD noise.
method Noise-averaging argument to regularize impact of non-classical noise.
result Established first finite-time moment bounds for SA under heavy-tailed and LRD noise.
The paper calculates option prices using Mellin transform for stochastic volatility models.
problem Calculating prices for path-dependent options under stochastic volatility.
method Asymptotic approach and Mellin transform for deriving closed-form formulas.
result Derives closed-form formulas for option prices with first-order approximation.
Proves global well-posedness for superquadratic BSDEs without Markovian assumption.
problem Global well-posedness of multidimensional superquadratic BSDEs without Markovian assumption.
method Interplay between local well-posedness of FBSDEs and backward iterations of superquadratic BSDEs.
result Global well-posedness of superquadratic BSDEs proved.
New copulas model multiple risk factors with tractable properties.
problem Modeling stochastic dependence in multiple risk factors.
method Introduce and study a new class of MRF copulas.
result MRF copulas are non-exchangeable and exhibit various tail dependences.
DeepONet accelerates reliability analysis of stochastic nonlinear systems.
problem Time-dependent reliability analysis of systems with stochastic forcing.
method DeepONet, a novel operator network, learns function-to-function mappings.
result DeepONet efficiently and accurately predicts system responses.
Proposes a new framework for optimizing utility with state-dependent benchmarks.
problem Various interpretations of benchmarks in utility functions.
method General framework of state-dependent utility optimization with stochastic benchmarks.
result Provides optimal solutions and addresses issues of well-definedness and feasibility.
A new model for limit order book dynamics with time-dependent arrival rates.
problem Modeling the dynamics of limit order books with time-dependent arrival rates.
method Proposes a stochastic model with endogenous price dynamics and shows the conditional diffusion limit is Brownian meander.
result The model's conditional diffusion limit is the Brownian meander.
Proves minimax sample complexity for turn-based stochastic games.
problem Proving theoretical guarantees for reinforcement learning in turn-based stochastic games.
method Developing absorbing TBSG and reward perturbation techniques to handle statistical dependence.
result Empirical Nash equilibrium strategy approximates true Nash equilibrium in turn-based stochastic games.
Entropy-minimal measure calculated for a stochastic volatility model.
problem Calculating the entropy-minimal equivalent martingale measure in a stochastic volatility model.
method Revised related theory, calculated entropy-minimal measure.
result Entropy-minimal measure for the exponential Ornstein-Uhlenbeck model.
The paper analyzes a class of stochastic games involving moving free boundaries and Nash equilibria.
problem Analyzing interactions among players in stochastic games with moving free boundaries.
method Deriving sufficient conditions for Nash equilibrium through verification theorems, solving multi-dimensional free boundary problems, and Skorokhod problems.
result An intriguing connection between NE strategies and controlled rank-dependent stochastic differential equations.
We reformulate data-dependent constraints to ensure they are always met with high probability.
problem Ensuring fairness and stability in machine learning models with data-dependent constraints.
method Calibrated reformulation of constraints to guarantee satisfaction with a specified probability.
result Our method guarantees that fairness constraints are met at test time with high probability.
New algorithms reduce regret in both stochastic and deterministic environments.
problem Designing algorithms that perform well in both types of MDPs.
method Proposed new environment norms and algorithms with variance-dependent regret bounds.
result First algorithm with simultaneously optimal bounds for both stochastic and deterministic MDPs.