New neural processes use stacked Markov operators to improve flexibility.
problem Improving flexibility in neural processes.
method Stacking neural parameterized Markov transition operators in function space.
result MNPs outperform baseline models on various tasks.
We study discretizations of polynomial processes using finite state Markov processes satisfying suitable moment matching conditions. The states of these Markov processes together with their transition probabilities can be interpreted as Markov cubature rules. The polynomial property allows us to study such rules using …
We prove that the variance swap rate (fair strike) equals the price of a co-terminal European-style contract when the underlying is an exponential Markov process, time-changed by an arbitrary continuous stochastic clock, which has arbitrary correlation with the driving Markov process, provided that the payoff function …
This paper applies AMP theory to improve learning tasks.
problem Improving learning efficiency by optimizing task-specific models.
method Uses aggregated Markov processes to reduce model complexity and enhance learning.
result Demonstrates how AMP theory can be effectively applied to stochastic learning.
New neural method for inferring Markov jump processes.
problem Inference in Markov jump processes is challenging.
method Variational inference using neural ODEs and backpropagation.
result Trains neural representations of data to approximate process rates.
Study of Markov-modulated affine processes for richer models in finance.
problem Richer models in various applications.
method Martingale problem approach, characteristic function derivation, mathematical properties study.
result Existence and characteristic function of Markov-modulated affine processes.
The Viterbi process can be extended indefinitely in a pairwise Markov model.
problem Estimating hidden chains in pairwise Markov models.
method Construction of barriers to ensure Viterbi path goes through states.
result The Viterbi process is regenerative in the PMM.
We introduce Markov substitute processes, a new model at the crossroad of statistics and formal grammars, and prove its main property : Markov substitute processes with a given support form an exponential family.
We review some developments concerning Markov and Feller processes with jumps in geometric settings. These include stochastic differential equations in Markus canonical form, the Courrège theorem on Lie groups, and invariant Markov processes on manifolds under both transitive and more general Lie group actions.
In this paper we propose a semi-Markov modulated model of interest rates. We assume that the switching process is a semi-Markov process with finite state space E and the modulated process is a diffusive process. We derive recursive equations for the higher order moments of the discount factor and we describe a Monte Ca…
Model credit ratings using economic states with Markov chains.
problem Credit rating migration influenced by economic state changes.
method Developed a Markov chain model for credit ratings conditional on economic states.
result Derived asymptotic behavior of the rating process using Markov theory.
New model for insurance states using Markov jump processes with non-countable state space.
problem Modeling insurance states with non-countable state spaces.
method Developed a new Thiele's differential equation for continuous time rehabilitation rates.
result Allows for consistent calculation of reserves in disability insurance.
New algorithm solves uncertain Markov decision processes using Wasserstein uncertainty.
problem Solving Markov decision processes with uncertain transition probabilities.
method Distributionally robust Q-learning algorithm for Wasserstein uncertainty. result Convergence of the algorithm proved and demonstrated with real data.
Paper proposes a new method for training diffusion models using Markov operators.
problem Training efficiency and accuracy in diffusion models.
method Operator-informed score matching using spectral decomposition of Markov operators.
result Improved score matching for both low and high-dimensional distributions.
Study approximates financial market with discrete-time models.
problem Approximating continuous-time financial market models with discrete-time.
method Constructs discrete-time market models with Markov switching and proves convergence.
result Discrete-time models converge to continuous-time Black-Scholes model with Markov switching.
Researchers calculate Shannon entropy rates of hidden Markov processes efficiently.
problem No finite expression exists for Shannon entropy rates of hidden Markov processes.
method Developed an efficient method to calculate entropy rates and identify minimal predictive features.
result Entropy rates can be accurately calculated for hidden Markov processes.
We introduce LAMP: the Linear Additive Markov Process. Transitions in LAMP may be influenced by states visited in the distant history of the process, but unlike higher-order Markov processes, LAMP retains an efficient parametrization. LAMP also allows the specific dependence on history to be learned efficiently from da…
This manuscript contributes a general and practical framework for casting a Markov process model of a system at equilibrium as a structural causal model, and carrying out counterfactual inference. Markov processes mathematically describe the mechanisms in the system, and predict the system's equilibrium behavior upon i…
Model reduction of Markov processes is a basic problem in modeling state-transition systems. Motivated by the state aggregation approach rooted in control theory, we study the statistical state compression of a discrete-state Markov chain from empirical trajectories. Through the lens of spectral decomposition, we study…
The generic identification problem is to decide whether a stochastic process (Xt) is a hidden Markov process and if yes to infer its parameters for all but a subset of parametrizations that form a lower-dimensional subvariety in parameter space. Partial answers so far available depend on extra assumptions on the pro…
Drawdown (resp. drawup) of a stochastic process, also referred as the reflected process at its supremum (resp. infimum), has wide applications in many areas including financial risk management, actuarial mathematics and statistics. In this paper, for general time-homogeneous Markov processes, we study the joint law of …
Model detects market anomalies using a Hawkes process with hidden Markov chain.
problem Detecting high-frequency market manipulation in cryptocurrency trades.
method Developed a Markov-modulated Hawkes process with piecewise constant excitation kernels.
result Demonstrated the model's effectiveness in detecting suspicious trading activities.
In this paper we present an algorithm for pricing barrier options in one-dimensional Markov models. The approach rests on the construction of an approximating continuous-time Markov chain that closely follows the dynamics of the given Markov model. We illustrate the method by implementing it for a range of models, incl…
Paper presents an algorithm for optimal regret in communicating Markov decision processes.
problem Achieving optimal regret in Markov decision processes with a communicating assumption.
method The algorithm explicitly tracks the constant K(M) to learn optimally, balancing exploration, co-exploration, and exploitation.
result The algorithm achieves asymptotically optimal regret K(M)log(T)+o(log(T)) for communicating Markov decision processes. Enhances count process modelling with Markov-modulated non-homogeneous Poisson process.
problem Count data modelling challenges, especially in complex scenarios.
method Introduces a flexible frequency perturbation measure into Markov-modulated Poisson process framework.
result Natural incorporation of observed event arrivals and latent factors.
In this paper we continue the study of the simulated stock market framework defined by the driving sentiment processes. We focus on the market environment driven by the buy/sell trading sentiment process of the Markov chain type. We apply the methodology of the Hidden Markov Models and the Recurrent Neural Networks to …
Algorithm learns mixtures of Markov chains and MDPs from short trajectories.
problem Learning mixtures of Markov chains and MDPs from short unlabeled trajectories.
method Subspace estimation, spectral clustering, EM algorithm, model estimation, classification.
result 96.6% average accuracy on a mixture of two MDPs in gridworld, outperforming EM algorithm with random initialization.
Modeling maximum drawdown records in capital markets using PDMP.
problem Capturing the statistical properties of maximum drawdown records in financial markets.
method Piecewise Deterministic Markov Process (PDMP) for modeling, statistical analysis of mean and variance, simulation study, parameter estimation techniques.
result Derivation of statistical results including mean and variance of maximum drawdown records.
Detects anomalies in multiple processes using hidden Markov models.
problem Detecting an anomalous process among many with hidden states.
method Sequential search strategy using ADHM algorithm.
result ADHM algorithm effectively leverages temporal correlations.
Unified approach to denoising Markov models for efficient sampling.
problem Designing efficient sampling algorithms for complex distributions.
method Mathematical foundation using measure transport and nonequilibrium statistical mechanics.
result Unified variational objective and backward generator construction.
We are interested in understanding stability (almost sure boundedness) of stochastic approximation algorithms (SAs) driven by a `controlled Markov' process. Analyzing this class of algorithms is important, since many reinforcement learning (RL) algorithms can be cast as SAs driven by a `controlled Markov' process. In t…
Cai, Song and Kou (2015) [Cai, N., Y. Song, S. Kou (2015) A general framework for pricing Asian options under Markov processes. Oper. Res. 63(3): 540-554] made a breakthrough by proposing a general framework for pricing both discretely and continuously monitored Asian options under one-dimensional Markov processes. In …
New self-exciting random evolutions (SEREs) for modeling traffic and transport processes.
problem Modeling self-exciting and clustering effects in traffic and transport processes.
method Introducing a new process based on a superposition of a Markov chain and a Hawkes process, and constructing self-exciting random evolutions (SEREs).
result Developed new models and limit theorems for SEREs, including averaging and diffusion approximation.
Method calculates Parisian stopping times and option prices using Markov chains.
problem Computing distribution and pricing of Parisian stopping times under Markov processes.
method Continuous-time Markov chain approximation to solve for distribution and convergence analysis.
result Sharp convergence rate and efficient method for diffusion and jump models.
Develops an actor-critic algorithm for risk-sensitive Markov decision processes.
problem Risk-sensitive cost criterion in Markov decision processes.
method Actor-critic algorithm with function approximation.
result Asymptotic convergence of the actor-critic algorithm.
Risk measures applied to dynamic Markov processes with varying risk aversion.
problem Investigating dynamic risk measures in Markov decision processes with varying risk aversion.
method Distributional viewpoint on law-invariant convex risk measures, applied to Markov decision processes with latent costs and random actions.
result Existence of optimal policies in finite and infinite time horizons under mild assumptions.
New method detects changes in high-dimensional Markov processes without explicit likelihood evaluation.
problem Quickest change detection in Markov processes with unknown transition kernels.
method Learn conditional score from sample pairs, develop score-based CUSUM procedure.
result Exponential lower bounds on mean time to false alarm and asymptotic upper bounds on detection delay.
Method reconstructs hidden Markov chains from insurance data.
problem Recovering hidden Markov chains from incomplete insurance data.
method Neural architecture to explicitly provide transition probabilities.
result Neural model successfully validates decompression of insurance information.
In most sampling algorithms, including Hamiltonian Monte Carlo, transition rates between states correspond to the probability of making a transition in a single time step, and are constrained to be less than or equal to 1. We derive a Hamiltonian Monte Carlo algorithm using a continuous time Markov jump process, and ar…
The study uses Markov chains to forecast cryptocurrency market dynamics.
problem Forecasting and understanding market fluctuations in cryptocurrencies.
method Markov chains of orders one to eight were used to forecast intra-day returns of three major cryptocurrencies.
result Predictions from empirical probabilities outperform random choices.
Overview of risk-sensitive Markov decision processes with Optimized Certainty Equivalent.
problem Optimizing decision-making under risk in Markov processes.
method Analyzes risk-sensitive criteria using Optimized Certainty Equivalent, including entropic risk and Conditional Value-at-Risk.
result Conditions for the existence of optimal policies and solution procedures are provided.
We consider Markov models of stochastic processes where the next-step conditional distribution is defined by a kernel density estimator (KDE), similar to Markov forecast densities and certain time-series bootstrap schemes. The KDE Markov models (KDE-MMs) we discuss are nonlinear, nonparametric, fully probabilistic repr…
Optimizes control of hybrid systems with multiple switching processes.
problem Optimal control of hybrid systems with multiple Markov switching processes.
method Combines two separate Markov chains into one synthetic chain, derives HJB equations, and solves the portfolio choice problem.
result Derives explicit solutions and value functions for the optimal control problem.
New algorithm identifies best policy in MDPs faster.
problem Identifying the best policy in Markov Decision Processes.
method Problem-dependent lower bound and first algorithm with instance-specific sample complexity.
result First algorithm with reduced exploration rate for faster convergence.
Study optimality in safety-constrained Markov decision processes using asynchronous value iteration and modified Q-learning.
problem Optimality in safety-constrained Markov decision processes with multichain structure.
method Formulated as a zero-sum game, constructed asynchronous value iteration scheme and modified Q-learning algorithm.
result Resolved Bellman's principle of optimality for multichain Markov decision processes and provided learning algorithms.
Bayesian MS-VAR process improves option pricing models.
problem Improving option pricing models for better accuracy.
method Bayesian Markov-Switching Vector Autoregressive (MS-BVAR) process with risk-neutral valuation.
result Derived pricing formulas for various options.
New entropy flow method extends generalization bounds for all Markov algorithms.
problem Understanding generalization error for Markov algorithms.
method Unified framework using continuous-time approximation and modified logarithmic Sobolev inequalities.
result Established new connections between generalization error and ergodic properties of Markov processes.
The Bivariate Dynamic Contagion Processes (BDCP) are a broad class of bivariate point processes characterized by the intensities as a general class of piecewise deterministic Markov processes. The BDCP describes a rich dynamic structure where the system is under the influence of both external and internal factors model…