Stochastic differential equation approximation for linear TD(0) under Markovian noise
problem Temporal-difference learning with linear function approximation
method Stochastic differential equation approximation
result Explains the constant-stepsize error floor
Extends pricing methods for index options under rough volatility.
problem Pricing and hedging of index options under non-Markovian dynamics.
method Extension of large deviations methods to non-local volatility dynamics, specifically rough volatility.
result Validates the approach for pricing index options under rough volatility.
Transformers struggle to learn Markovian dynamics, showing NP-hard optimization challenges.
problem Understanding transformers' limitations in learning Markovian dynamical functions.
method Investigated through a structured ICL setup, analyzing loss landscapes and parameter optimization.
result Recovering optimal transformer parameters for Markovian functions is NP-hard.
This paper solves the inversion problem for jump processes using Markovian projections.
problem Calibrating jump-diffusion models with both local and stochastic features.
method Inverting Markovian projections for pure jump processes.
result Constructs calibrated local stochastic intensity (LSI) models for credit risk applications.
Kernel analog forecasting studied for multiscale systems.
problem Interpreting data-driven predictions in multiscale dynamical systems.
method Kernel analog forecasting methods applied to multiscale systems with varying Markovian closures.
result Guidance provided for interpreting data-driven predictions in practice.
Extends Hawkes process for flexible residual modeling in point processes.
problem Modeling high-frequency financial data with complex residual distributions.
method Introduces self and mutually exciting point process with discretely Markovian dynamics.
result Flexible residual distributions improve intensity modeling and high-frequency data estimation.
Modeling high-frequency order book data with Hawkes-Markovian process.
problem Capturing the dynamics of high-frequency order book events.
method Hawkes process with Markovian baseline intensities, LASSO regularization, and Akaike Information Criteria.
result Effective modeling of order book dynamics with reduced parameter redundancy.
New method learns dynamic brain communication patterns across regions.
problem Current methods struggle with time-varying brain communications and scalability.
method Adaptive Delay Model (ADM) using Markovian Gaussian Processes.
result Captures dynamic neural communication patterns over time.
Markovian RNN adapts to nonstationary data using HMM for better time series prediction.
problem Nonstationary sequential data in real-life applications.
method Markovian RNN with HMM for regime switching and end-to-end optimization.
result Significant performance gains over vanilla RNN and Markov Switching ARIMA.
This paper studies the equilibrium pricing of asset shares in the presence of dynamic private information. The market consists of a risk-neutral informed agent who observes the firm value, noise traders, and competitive market makers who set share prices using the total order flow as a noisy signal of the insider's inf…
We develop a Markovian approximation for SVV models to compute hedging strategies.
problem Computing optimal hedging strategies for SVV models with non-Markovian noise.
method Develop a Markovian approximation of the Volterra noise kernel to compute hedging strategies.
result Error estimates for the approximation of volatility, prices, and optimal hedge.
A new HOM model improves forecasting of Indian base metal prices.
problem Improving accuracy in predicting base metal prices in the Indian market.
method A Higher Order Markovian (HOM) model with varying order based on market delay.
result The HOM model consistently outperforms the standard Markovian model in forecasting.
New method for pricing European options in rough LSV models.
problem Pricing European options in non-Markovian local stochastic volatility models.
method Conditional LSV dynamics, rough path theory, rough partial differential equations (RPDEs).
result Established a PDE pricing method for non-Markovian models.
Paper tackles non-Markovian control problems with new learning methods.
problem Non-Markovian stochastic control problems with unknown parameters.
method Off-model training and importance sampling for deep neural network approximation.
result Quantitative error bounds for adaptive learning under model uncertainty.
Study improves covariance estimation for SGD under Markovian data, matching best rates.
problem Improving covariance estimation for SGD in Markovian data settings.
method Online overlapping batch-means covariance estimator for SGD under Markovian sampling.
result Established convergence rates for covariance estimation under Markovian sampling.
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 Z−constrained BSDE, with dynamics associated to a non singular underlying forward process. Du…
A new method predicts non-Markovian closure terms for complex systems.
problem Predicting the effect of unresolved variables on resolved dynamics in high-dimensional systems.
method Mamba-Assisted Closure (MAC) framework: sequence model trained to predict closure from resolved trajectory, coupled with reduced-order equations.
result Substantially outperforms existing methods in predictive accuracy and long-time stability.
Path signatures improve hedging of exotic derivatives in non-Markovian models.
problem Hedging exotic derivatives under non-Markovian stochastic volatility models.
method Investigates path signatures in deep and shallow learning contexts, comparing neural networks and regression approaches.
result Path signatures outperform LSTM in most cases and yield more accurate results in hedging.
DAMNETS generates complex network dynamics models.
problem Generating flexible and scalable models for network time series is challenging.
method Deep autoregressive model for Markovian network time series.
result DAMNETS outperforms other methods in sample quality.
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.
Study designs incentives for adapting multi-agent systems without knowing their learning dynamics.
problem Designing incentives for an adapting population in multi-agent systems without prior knowledge of their learning dynamics.
method Introduces a model-based non-episodic Reinforcement Learning (RL) formulation for steering Markovian agents towards desired policies, focusing on history-dependent strategies to handle model uncertainty.
result Identifies conditions for the existence of steering strategies to guide agents to desired policies and provides empirical algorithms to approximately solve the objective.
Study on learning to predict dynamical systems without assuming their structure.
problem Learning to predict the next state of a dynamical system with unknown evolution function.
method Defined new combinatorial measures to quantify mistake and regret bounds in realizable and agnostic settings.
result In the realizable setting, the number of mistakes can grow arbitrarily with time.
Estimates hybrid dynamical systems with polynomial expansions and Markovian switching.
problem Identifying hybrid dynamical systems with nonlinear autoregressive exogenous (NARX) components and Markovian switching.
method Probabilistic framework using Expectation Maximization for parameter estimation, including submodel coefficients, hidden state values, and transition probabilities. Disentangles mode classification and NARX regression tasks. Uses soft-labels and coordinate descent approach for parameter fitting.
result Demonstrated on a SMNARX problem with three nonlinear sub-models, achieving parsimonious models through l1-norm bridge estimation and hard-thresholding.
Study optimal portfolios in a non-Markovian regime-switching model with random time horizon.
problem Optimal portfolio selection in a market with non-Markovian regime-switching and random time horizon.
method Formulated as a constrained stochastic linear-quadratic optimal control problem, derived closed-form expressions for optimal portfolios and efficient frontier.
result Closed-form expressions for optimal portfolios and efficient frontier derived under non-Markovian regime-switching and random time horizon.
HS-FNO models non-Markovian PDEs by learning history and future states.
problem Non-Markovian dynamics where future states depend on past history.
method History-Space Fourier Neural Operator (HS-FNO) for delay and memory-driven PDEs.
result HS-FNO achieves lowest aggregate errors across various PDE families.
Inference, prediction and control of complex dynamical systems from time series is important in many areas, including financial markets, power grid management, climate and weather modeling, or molecular dynamics. The analysis of such highly nonlinear dynamical systems is facilitated by the fact that we can often find a…
We propose and study a simple stochastic model for the dynamics of a limit order book, in which arrivals of market order, limit orders and order cancellations are described in terms of a Markovian queueing system. Through its analytical tractability, the model allows to obtain analytical expressions for various quantit…
Breaks down complex nonlinear dynamics into simpler components.
problem Control of nonlinear dynamical systems remains challenging.
method Inspired by hybrid switching systems, decomposes dynamics into simpler stochastic switching linear dynamical systems.
result Extracts hierarchies of Markovian and auto-regressive locally linear controllers from nonlinear experts.
Paper analyzes CLT for TTSA with Markovian noise, broadening its applications.
problem Analyzing asymptotic behavior of TTSA under Markovian noise.
method Central Limit Theorem applied to TTSA with Markovian noise.
result Uncovered coupled dynamics of TTSA influenced by Markov chain.
Develops a kernel-based framework for dynamic trading strategies.
problem Optimizing portfolios with temporal dependencies in asset dynamics.
method Parameterizes trading strategies as functions in RKHS, enabling flexible, non-Markovian approaches.
result Significantly outperforms classical Markovian methods in synthetic and market-data examples.
Develops RL algorithm for non-Markovian, non-stationary reward streams.
problem Maximizing rewards from non-Markovian, non-stationary reward streams.
method Uses causal DAG to construct Markov states, solves periodic MDP.
result Optimal state construction maximizes discounted rewards.
Study analyzes non-Markovian effects in financial markets over multiple years.
problem Understanding non-Markovian dynamics and trader interactions in financial markets.
method Empirical analysis of self-response functions and trade sign correlators for different stocks over multiple years.
result Significant variations in traders' interactions over time, indicating changes in market mechanisms.
Paper improves neural ODEs for forecasting non-Markovian processes.
problem Forecasting irregularly observed time series with incomplete data.
method Path-dependent Neural Jump ODEs with signature transform.
result Path-dependent NJ-ODE outperforms original framework in non-Markovian data.
PMP extends GNNs to handle past states efficiently.
problem Efficient querying of data structures dependent on previous states.
method Persistent Message Passing (PMP) which persists past states through new nodes.
result Significantly outperforms GNNs in handling out-of-distribution data.
New algorithm solves complex stopping problems with robust optimization.
problem Solving complex stochastic optimal stopping problems.
method Simulation-based robust optimization with exact reformulation as a zero-one bilinear program.
result Developed polynomial-time heuristics and algorithms for practical solution.
The paper analyzes trade execution strategies for large traders in a stochastic market environment.
problem Analyzing trade execution strategies in a stochastic market with price impact.
method Formulated a Markov game model and used backward induction method of dynamic programming.
result Explicit closed-form execution strategy at Markov perfect equilibrium.
The paper develops methods to price options under rough volatility models using BSPDEs.
problem Pricing options in models with non-Markovian dynamics.
method Backward stochastic partial differential equations (BSPDEs) and deep learning for numerical approximations.
result Existence and uniqueness of weak solutions for general nonlinear BSPDEs.
BSLP is a two-dimensional dynamic model of interacting portfolio-level loss and spread (more exactly, loss intensity) processes. The model is similar to the top-down HJM-like frameworks developed by Schonbucher (2005) and Sidenius-Peterbarg-Andersen (SPA) (2005), however is constructed as a Markovian, short-rate intens…
We consider the problem of constructing an appropriate multivariate model for the study of the counterparty credit risk in credit rating migration problem. For this financial problem different multivariate Markov chain models were proposed. However the markovian assumption may be inappropriate for the study of the dyna…
This paper studies a portfolio optimization problem in a discrete-time Markovian model of a financial market, in which asset price dynamics depend on an external process of economic factors. There are transaction costs with a structure that covers, in particular, the case of fixed plus proportional costs. We prove that…
Paper introduces MVS to detect non-Markovian observations in reinforcement learning.
problem Real-world sensors violate Markov property, leading to suboptimal reinforcement learning performance.
method Uses prediction-based Markov Violation Score (MVS) combining random forest and ridge regression.
result MVS detects non-Markovian structure in observation trajectories, quantifying its impact.
New estimator reduces bias-variance tradeoff in Markovian interference experiments.
problem Estimating impact of interventions in systems with limited resources.
method Differences-In-Q (DQ) estimator for on-policy policy evaluation.
result DQ estimator has exponentially smaller variance than off-policy methods.
Unified model for market dynamics, linking price and order flow.
problem Modeling market dynamics and order flow in a unified framework.
method Markovian market model driven by a hidden Brownian efficient price, signal-driven and queue-reactive models.
result Stability of mid-price around efficient price at macroscopic scale, behavior as diffusion.
Non-Markovian point process shows power-law scaling, similar to nonlinear Markovian process.
problem Understanding the scaling behavior of non-Markovian point processes.
method Analyzed a confined fractional Brownian motion-driven point process and compared it to a nonlinear Markovian process.
result A nonlinear Markovian process can reproduce the power-law scaling behavior of a non-Markovian point process.
Novel method learns time series dynamics without reconstruction.
problem Learning nonlinear stochastic dynamics from video data.
method Recognition-parametrized Gaussian state space model (RP-GSSM) using maximum likelihood.
result Outperforms alternatives on nonlinear stochastic dynamics learning.
New RL algorithms correct bias in dynamic data analysis.
problem Dynamic data generation and analysis create endogeneity issues.
method Instrument variable (IV)-based reinforcement learning (RL) algorithms.
result Established theoretical properties of IV-RL algorithms.
A new growth model for dynamic networks using Markovian latent points.
problem Modeling temporal dynamic networks with latent points and distances.
method Markovian latent space dynamic with Euclidean Sphere sampling and connection probabilities based on geodesic distances.
result Theoretical guarantees for non-parametric estimation of the latitude and envelope functions.
Projects Markovian processes from Itô semimartingales with jumps.
problem Modeling Itô semimartingales with jumps using Markovian projections.
method Construct Markovian projections for Itô semimartingales with jumps using non-local FPKEs.
result Markovian projections match the marginal laws of the original process.