Paper introduces PRMs to learn non-Markovian stochastic rewards for reinforcement learning.
problem Lack of structured representation for non-Markovian stochastic rewards in reinforcement learning.
method Introduces probabilistic reward machines (PRMs) and presents an algorithm to learn them from decision processes.
result Algorithm proves correct and convergent for learning PRMs from decision processes.
The purpose of this article is to describe all possible beliefs of market participants on objective measures under Markovian environments when a risk-neutral measure is given. To achieve this, we employ the Martin integral representation of Markovian pricing kernels. Then, we offer economic and financial implications o…
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.
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…
Representation learning on networks offers a powerful alternative to the oft painstaking process of manual feature engineering, and as a result, has enjoyed considerable success in recent years. However, all the existing representation learning methods are based on the first-order network (FON), that is, the network th…
Developed scalable Monte Carlo method for VIX option pricing.
problem VIX option pricing in stochastic Volterra rough volatility models with non-Markovian vol-of-vol.
method Infinite dimensional Markovian representation to devise scalable least squares Monte Carlo.
result Efficient VIX option pricing method for generalized models.
A new method scales Gaussian process variational autoencoders to handle high-dimensional time series.
problem Scalability issue in Gaussian process variational autoencoders (GPVAEs).
method Introducing Markovian GPs and using Kalman filtering and smoothing for linear time training.
result MGPVAE outperforms existing approaches in various tasks with high scalability.
Many fractional processes can be represented as an integral over a family of Ornstein-Uhlenbeck processes. This representation naturally lends itself to numerical discretizations, which are shown in this paper to have strong convergence rates of arbitrarily high polynomial order. This explains the potential, but also s…
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.
New framework for policy gradient methods in continuous time reinforcement learning.
problem Addressing policy gradient methods for continuous time reinforcement learning.
method Control randomisation technique to derive policy gradient representation for various Markovian control problems.
result Demonstrated application to optimal switching problems in the energy sector.
Most real-world problems have huge state and/or action spaces. Therefore, a naive application of existing tabular solution methods is not tractable on such problems. Nonetheless, these solution methods are quite useful if an agent has access to a relatively small state-action space homomorphism of the true environment …
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.
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.
The paper analyzes multivariate payments in multi-state life insurance using Markovian state processes.
problem Analyzing joint effects of life annuities and death benefits in a multi-state framework.
method Introduces multivariate present value of future payments, derives differential equations and moment generating functions, and focuses on pair-wise covariances.
result Derives Hattendorff type results for pair-wise covariances in a disability model.
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.
A new metric detects non-Markovian states in partially observable environments.
problem Learning state representations in partially observable environments.
method Introducing the λ-discrepancy metric to detect non-Markovian states. result The λ-discrepancy is zero for Markov processes and non-zero for partially observable environments. We review the problem of defining and inferring a "state" for a control system based on complex, high-dimensional, highly uncertain measurement streams such as videos. Such a state, or representation, should contain all and only the information needed for control, and discount nuisance variability in the data. It shoul…
This paper extends Markovian projections to semimartingales with jumps.
problem Extending Markovian projections to semimartingales with jumps.
method Using Markovian projections to match marginal laws of Itô semimartingales with jumps.
result Existence of Markovian projections for Itô semimartingales with jumps.
Study optimizes portfolio to minimize relative drawdown duration, penalizing unfavorable performance states.
problem Minimizing relative drawdown duration in portfolio optimization relative to a benchmark.
method Introduces a benchmark-relative drawdown-duration criterion penalizing unfavorable performance states. Uses a one-dimensional Markovian representation and Hamilton-Jacobi-Bellman equation.
result Derives explicit projection-based characterization of the optimal feedback control and identifies geometric settings for unique strong solutions.
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.
Analyzes non-Markovian environments in stochastic approximation.
problem Understanding learning mechanisms in non-ergodic, non-Markovian settings.
method Analytic framework for transformer learning and continual learning.
result Proposes a new approach to transformer and continual learning.
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
Paper establishes convergence rates and concentration bounds for stochastic approximation and reinforcement learning with Markovian noise.
problem Analyzing convergence rates and concentration bounds for stochastic approximation and reinforcement learning with Markovian noise.
method Novel discretization of the mean ODE of stochastic approximation algorithms using intervals with diminishing length.
result First almost sure convergence rate and maximal concentration bound with exponential tails for contractive stochastic approximation algorithms with Markovian noise.
New hierarchical VQ-VAE scheme improves image compression quality and features at low bitrates.
problem Low bitrate image compression maintaining quality and features.
method Hierarchical VQ-VAE with stochastic quantization and Markovian latent variables.
result High perceptual quality and semantic features at low bitrates.
Unified analytical tool for non-Markovian jump processes.
problem Analyzing history-dependent jump processes with non-Markovian behavior.
method Developed a standard form of master equations using Laplace-space embedding and asymptotic solution.
result Unified analytical toolset for general non-Markovian processes, leading to the GLE approximation.
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.
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.
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.
Describes state variables in sequential decision problems, linking them to Markovian and non-Markovian models.
problem Sequential decision problems, especially in active learning and POMDPs, where decisions affect what is observed and learned.
method Canonical framework and novel two-agent perspective of POMDPs, defining state variables to claim Markovian or non-Markovian models.
result Properly modeled sequential decision problems are Markovian, while real decision problems are often non-Markovian.
Deep learning solves non-Markovian FBSDEs for utility maximization.
problem Solving utility maximization problems under rough volatility.
method Deep learning-based numerical methods for non-Markovian fully coupled FBSDEs.
result Error estimates and convergence provided for the deep learning approach.
Investigates optimal consumption and investment strategies in non-Markovian markets with unbounded parameters.
problem Optimal consumption and investment strategies in non-Markovian markets with unbounded parameters.
method Martingale optimal principle and quadratic BSDEs with exponential moment.
result Establishes optimal strategies for consumption and investment.
We simplify a complex volatility model to make it easier to price options.
problem The rough Bergomi model's non-Markovian nature complicates option pricing.
method We approximate the rBergomi model with a Bergomi model that is Markovian.
result The rBergomi model can be effectively approximated by a Markovian model.
Fractional processes have gained popularity in financial modeling due to the dependence structure of their increments and the roughness of their sample paths. The non-Markovianity of these processes gives, however, rise to conceptual and practical difficulties in computation and calibration. To address these issues, we…
This paper first describes a class of uncertain stochastic control systems with Markovian switching, and derives an Itô-Liu formula for Markov-modulated processes. And we characterize an optimal control law, which satisfies the generalized Hamilton-Jacobi-Bellman (HJB) equation with Markovian switching. Then, by using …
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.
Improved SGD bounds for machine learning models with Markovian noise.
problem Uniform high-probability bounds for SGD under PL condition with Markovian noise.
method Combining Poisson equation for Markovian noise and probabilistic induction for almost-sure bounds.
result Matching 1/k decay rate for expected suboptimality. This paper addresses parameter estimation for wave equations with Markovian switching.
problem Parameter estimation for wave equations with abrupt changes.
method Bayesian statistical framework using discrete sparse Bayesian learning.
result Strong performance in parameter estimation for variable coefficient PDEs.
Paper derives convergence rates and confidence intervals for LSA with Markovian noise.
problem Analyzing convergence rates and constructing confidence intervals for LSA with Markovian noise.
method Derives non-asymptotic Berry-Esseen bounds and multiplier block bootstrap procedure.
result Provides O(n−1/4) convergence rates and guarantees consistent inference. 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.
We present a general Markovian framework for order book modeling. Through our approach, we aim at providing a tool enabling to get a better understanding of the price formation process and of the link between microscopic and macroscopic features of financial assets. To do so, we propose a new method of order book repre…
Paper tackles robust offline RL for non-Markovian processes, improving efficiency and applicability.
problem Learning robust policies for non-Markovian decision processes with limited offline data.
method Proposes a novel algorithm with dataset distillation and LCB design for robust values, derived new dual forms, and introduces concentrability coefficients.
result Proves polynomial sample efficiency for finding ε-optimal robust policies.
Paper provides exponential convergence guarantees for Iterative Markovian Fitting.
problem Addressing the Schrödinger Bridge problem in computational optimal transport and generative modeling.
method Develops non-asymptotic exponential convergence guarantees for Iterative Markovian Fitting.
result First non-asymptotic exponential convergence guarantees for IMF under mild structural assumptions.
We give a complete characterization of the sampling complexity of best Markovian arm identification in one-parameter Markovian bandit models. We derive instance specific nonasymptotic and asymptotic lower bounds which generalize those of the IID setting. We analyze the Track-and-Stop strategy, initially proposed for th…
Paper examines constant stepsize in LSA for Markovian data inference.
problem Improving statistical inference with constant stepsize in LSA for Markovian data.
method Established CLT, used averaged LSA iterates, applied Richardson-Romberg extrapolation.
result Constant stepsize leads to better CI coverage, especially with limited data.
Unified approach for first-order methods with Markovian noise in stochastic optimization and variational inequalities.
problem Stochastic optimization problems with Markovian noise.
method Unified theoretical analysis of first-order gradient methods using randomized batching and multilevel Monte Carlo.
result Optimal (linear) dependence on the mixing time of the noise sequence, eliminating previous limiting assumptions.
We show that when the price process S represents a fully incomplete market, the optimal super-replication of any Markovian claim g(ST) with g(⋅) being nonnegative and lower semicontinuous is of buy-and-hold type. Since both (unbounded) stochastic volatility models and rough volatility models are examples of …
Study finds rough volatility models underperform in SPX option pricing.
problem Inconsistency of rough volatility models with SPX option prices.
method Empirical study using SPX options data, comparing rough and Markovian models.
result Rough volatility models with H∈(0,1/2) are inconsistent with SPX smiles, especially at short maturities.