Consider power utility maximization of terminal wealth in a 1-dimensional continuous-time exponential Levy model with finite time horizon. We discretize the model by restricting portfolio adjustments to an equidistant discrete time grid. Under minimal assumptions we prove convergence of the optimal discrete-time strate…
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48 results for “discrete time models”
Discrete-time weak approximation of a Black-Scholes model with drift and volatility Markov switchingmath.PR
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.
Study of discrete-time mean-variance model using reinforcement learning.
problem Discrete-time model with more general return distribution assumptions.
method Entropy-based exploration cost, reinforcement learning algorithm design.
result Optimal investment strategy with Gaussian density function.
Faster sampling in discrete diffusion models with predetermined transition time.
problem Efficiency in sampling discrete diffusion models.
method Discrete Non-Markov Diffusion Models (DNDM) with predetermined transition time.
result Significantly reduces the number of function evaluations for faster sampling.
Continuous time framework for discrete data denoising models.
problem Efficient training and sampling for discrete data denoising models.
method Formulated as Continuous Time Markov Chains (CTMCs), efficient training using continuous time ELBO, high-dimensional CTMC simulation, novel theoretical error bound.
result Continuous time treatment enables novel theoretical error bound between generated and true data distributions.
Time series data that are not measured at regular intervals are commonly discretized as a preprocessing step. For example, data about customer arrival times might be simplified by summing the number of arrivals within hourly intervals, which produces a discrete-time time series that is easier to model. In this abstract…
This paper studies the properties of discrete time stochastic optimal control problems associated with portfolio selection. We investigate if optimal continuous time strategies can be used effectively for a discrete time market after a straightforward discretization. We found that Merton's strategy approximates the per…
Study proves existence and convergence of discrete-time Kyle models with multiple insiders.
problem Existence and convergence of discrete-time Kyle models with multiple informed traders.
method Proves existence and convergence of discrete-time Kyle models with multiple informed traders using mathematical proofs.
result Equilibrium exists and converges to continuous-time equilibrium as the number of trading times increases.
Defines speculative bubbles in discrete-time models based on discounted stock price losing mass.
problem Characterizing speculative bubbles in discrete-time models.
method Introduces a new definition based on discounted stock price behavior and provides probabilistic characterizations.
result Speculative bubbles in discrete time are linked to solutions of a linear Volterra integral equation.
This paper analyzes discrete diffusion models, deriving convergence bounds for their generated samples.
problem Theoretical guarantees for discrete-state diffusion models remain under-explored.
method Continuous Time Markov Chain (CTMC) framework and discrete-time sampling algorithm.
result Convergence bounds for KL divergence and TV distance are derived, showing linear dependence on dimension.
Masking diffusion outperforms other discrete diffusion models by incorporating jump times into the model.
problem Improving the performance of discrete diffusion models.
method Conditioning on the jump schedule of discrete Markov processes.
result Schedule-conditioned discrete diffusion (SCUD) models outperform classical and masking diffusion models.
A new RG approach connects discrete and continuous time descriptions of Gaussian processes.
problem Discretization of continuous stochastic processes for accurate simulation or model inference.
method Renormalization Group (RG) approach for Gaussian time series generated by auto-regressive models.
result RG fixed points correspond to discretizations of linear SDEs, providing insights into process accuracy.
PyDTS analyzes survival data with discrete intervals and competing risks.
problem Discrete-time survival analysis with competing risks and optional penalization.
method Regularized estimation methods, model evaluation metrics, variable screening tools, and simulation module.
result Supports research and development in discrete-time survival analysis.
A new model for time series using discrete latent states.
problem Efficiently modeling time series data with discrete latent states.
method A Markov chain-based model for training high-dimensional discrete latent data.
result Improved performance on time series datasets.
Corrected samplers reduce discretization error in discrete flow models without additional computational cost.
problem Discretization error in samplers for discrete flow models.
method Established non-asymptotic error bounds for samplers, proposed time-corrected and location-corrected samplers.
result Location-corrected sampler has lower complexity and better generation quality.
Paper analyzes symbolic-dynamics inspired Markov modeling for time-series data.
problem Capturing temporal patterns in sequential data for statistical learning.
method Two-step process: discretization of continuous attributes and estimation of temporal memory.
result Effective Markov modeling depends on accurate discretization and memory estimation.
Reinforcement Learning for a Discrete-Time Linear-Quadratic Control Problem with an Applicationstat.ML
RL solves discrete LQ control with Gaussian optimal policy.
problem Discrete-time linear-quadratic control problem.
method Entropy-based RL to find Gaussian optimal policy.
result RL algorithm solves mean-variance asset-liability management problem.
This work compresses sequences by treating them as continuous-time processes, enabling efficient discretization.
problem Efficient compression of sequences, especially with deep learning models that scale with sequence length.
method Treat sequences as continuous-time processes, learn efficient discretization, and decode at different time intervals.
result Automatic bit rate reductions in video and motion capture sequences using learned discretization.
Inference, Prediction, and Entropy-Rate Estimation of Continuous-time, Discrete-event Processescond-mat.stat-mech
New methods for inferring, predicting, and estimating continuous-time, discrete-event processes.
problem Inferring, predicting, and estimating entropy rate of continuous-time, discrete-event processes.
method Bayesian structural inference extended with neural networks.
result Methods are competitive for prediction and entropy-rate estimation with state-of-the-art.
Unified discrete diffusion for categorical data simplifies training and sampling.
problem Training and sampling in discrete diffusion models for categorical data.
method Mathematical simplifications and elegant unification of discrete-time and continuous-time discrete diffusion.
result Unified Simplified Discrete Denoising Diffusion (USD3) outperforms SOTA baselines.
Safety filter for unknown discrete-time systems with learned models and noise covariance.
problem Ensuring safety for unknown discrete-time linear systems with Gaussian noise.
method Develops a learning-based safety filter using empirical model and noise covariance, optimizing control actions to stay within safety constraints.
result Minimally modifies nominal control actions to ensure safety with high probability, tightening constraints as more data is collected.
Paper develops a continuous-time framework for financial markets without stochastic calculus.
problem Developing continuous-time financial models without stochastic calculus.
method A general framework using conditional topologies and pseudo-distance topologies.
result No-arbitrage conditions hold in continuous time if and only if they hold in discrete time.
The paper studies market viability and completeness in discrete markets.
problem Characterizing the set of equivalent martingale measures in finite markets.
method Characterization as convex combinations of martingale measures, algorithm for finding these measures.
result Limitations of using discrete-time models to understand continuous-time models.
In this article we discuss the problem of calculating optimal model-independent (robust) bounds for the price of Asian options with discrete and continuous averaging. We will give geometric characterisations of the maximising and the minimising pricing model for certain types of Asian options in discrete and continuous…
We develop theory and applications of forward characteristic processes in discrete time following a seminal paper of Jan Kallsen and Paul Krühner. Particular emphasis is placed on the dynamics of volatility surfaces which can be easily formulated and implemented from the chosen discrete point of view. In mathematical t…
Study improves sampling efficiency of diffusion models using RL and PDEs.
problem Training neural stochastic differential equations without access to target samples.
method Proves equivalences between RL methods and PDEs, uses coarse time discretization.
result Improves sample efficiency and reduces computational cost.
We consider a discrete-time financial market model with finite time horizon and give conditions which guarantee the existence of an optimal strategy for the problem of maximizing expected terminal utility. Equivalent martingale measures are constructed using optimal strategies.
New discrete models for constant mean curvature surfaces and tori.
problem Creating discrete models for constant mean curvature surfaces and tori.
method Integrable theory of discrete polarised curves and Darboux transforms.
result Closed-form discrete parametrisations of discrete isothermic cylinders, discrete constant mean curvature cylinders, and discrete isothermic tori.
Paper introduces DMPMs for efficient discrete data generation with sharp convergence bounds.
problem Efficient generation of discrete data with theoretical guarantees.
method Discrete Markov Probabilistic Models (DMPMs) operating in bit space with time-reversal process.
result Sharp convergence bounds established under minimal assumptions, competitive performance in discrete data generation.
Convergence Analysis of Discrete Diffusion Model: Exact Implementation through Uniformizationstat.ML
Discrete diffusion models improve data generation for discrete data like language and graphs.
problem Adapting diffusion models to discrete state spaces for better data generation.
method Formulated as CTMCs, used uniformization of continuous Markov chains for sampling.
result Derive guarantees for sampling from any distribution on a hypercube, aligning with state-of-the-art achievements.
Characterizes super-replication prices in a financial market model.
problem Characterizing prices in a financial market model.
method Characterizes prices as the supremum of mono-prior super-replication prices through extreme priors and martingale measures.
result Super-replication prices are the supremum of mono-prior super-replication prices.
Discrete Adjoint Matchingstat.ML
Proposes DAM for optimizing discrete generative models.
problem Challenges in optimizing discrete generative models.
method Discrete Adjoint Matching (DAM) for discrete state spaces.
result Demonstrates effectiveness on synthetic and mathematical reasoning tasks.
NCDSSM models irregularly sampled time series with improved imputation and forecasting.
problem Accurate modeling of irregularly sampled time series with missing observations.
method Neural Continuous-Discrete State Space Model (NCDSSM) with amortized inference for auxiliary variables and flexible dynamic state parameterizations.
result Improved imputation and forecasting performance on multiple benchmark datasets.
A new model predicts discrete events with flexible, nonparametric baseline and excitation.
problem Limited flexibility in discrete Hawkes models for event prediction.
method Gaussian Process Discrete Hawkes Process (GP-DHP) with collapsed latent representation.
result Improves predictive log-likelihood for diverse event patterns.
The discrete-time GARCH methodology which has had such a profound influence on the modelling of heteroscedasticity in time series is intuitively well motivated in capturing many `stylized facts' concerning financial series, and is now almost routinely used in a wide range of situations, often including some where the d…
We study asymptotic properties of some (essentially conditional least squares) parameter estimators for the subcritical Heston model based on discrete time observations derived from conditional least squares estimators of some modified parameters.
This study bridges discrete and continuous state spaces using the Ehrenfest process and diffusion models.
problem Understanding the relationship between discrete and continuous state spaces in stochastic processes.
method Investigates time-continuous Markov jump processes on discrete state spaces and their correspondence to state-continuous diffusion processes.
result The time-reversal of the Ehrenfest process converges to the time-reversed Ornstein-Uhlenbeck process, bridging discrete and continuous state spaces.
PAGP uses physics-assisted Gaussian processes to solve and learn PDEs.
problem Solving and discovering unknown coefficients in PDEs with initial and boundary conditions.
method Physics-assisted Gaussian processes with continuous, discrete, and hybrid models.
result Effective in solving and discovering unknown coefficients in PDEs.
Structural and Convergence Analysis of Discrete-Time Denoising Diffusion Probabilistic Modelsmath.PR
The paper analyzes the probabilistic structure of DDPMs and bounds their sampling error.
problem Understanding and controlling errors in discrete-time DDPMs.
method Structural analysis of score functions, Schrödinger's problem, and FBSDEs.
result Explicit upper bound for total variation distance between sampling and target distributions.
There is a need for the development of models that are able to account for discreteness in data, along with its time series properties and correlation. Our focus falls on INteger-valued AutoRegressive (INAR) type models. The INAR type models can be used in conjunction with existing model-based clustering techniques to …
Continuous-time MBRL framework tackles control systems with Bayesian ODEs.
problem Discretization of continuous-time systems in MBRL.
method Novel actor-critic method with Bayesian ODEs for state inference.
result Model robust against irregular and noisy data, sample-efficient, solves challenging control problems.
MOB-dS uses permutation to correct for dependency in discrete survival data.
problem Identifying subgroups in discrete event time data with potential spurious results.
method Model-based recursive partitioning (MOB) with modified data matrix and permutation test.
result MOB-dS controls type I error rate better than standard MOB for discrete survival data.
Study optimal hedging for claims with random weights in discrete time.
problem Optimal hedging for claims with random weights in discrete time.
method Explicit recursive representation of optimal hedging strategy, without ND condition.
result Obtained explicit optimal hedging strategy in a recursive form.
Optimal strategy for liquidating portfolios under discrete time intervals.
problem Optimizing liquidation of portfolios with discrete time constraints and impact effects.
method Modeling portfolio liquidation with N risky assets, using VaR for cost measurement, and deriving an optimal liquidation time.
result The optimal liquidation time is only influenced by temporary price impacts, not permanent ones.
Extends Neural ODEs to model discrete changes in continuous systems.
problem Lack of explicit termination time in existing Neural ODE formulations.
method Introduces neural event functions to implicitly define termination criteria.
result Models discrete changes in continuous systems without prior knowledge.
In this work, we consider the hedging error due to discrete trading in models with jumps. Extending an approach developed by Fukasawa [In Stochastic Analysis with Financial Applications (2011) 331-346 Birkhäuser/Springer Basel AG] for continuous processes, we propose a framework enabling us to (asymptotically) optimize…
New method for discrete-time survival analysis with competing risks.
problem Discrete failure time data in survival analysis.
method Proposes a new estimation procedure for discrete-time survival analysis with competing events.
result Offers advantages over existing procedures and integrates regularized regression methods.
This paper derives a diffusion approximation for a sequence of discrete-time one-sided limit order book models with non-linear state dependent order arrival and cancellation dynamics. The discrete time sequences are specified in terms of an -valued best bid price process and an -valued volume process. …