arXiv research

Paper introduces infinite-dimensional generative models using Doob's h-transform.

New method aligns diffusion models for inference-time properties without retraining.

New algorithm learns bridged diffusion processes without time-reversals.

New method simulates diffusion bridges using score matching.

In the paper, we introduce the notion of a local regular supermartingale relative to a convex set of equivalent measures and prove for it an optional Doob decomposition in the discrete case. This Theorem is a generalization of the famous Doob decomposition onto the case of supermartingales relative to a convex set of e…

We present a unified approach to Doob's $L^p$ maximal inequalities for $1\leq p<\infty$. The novelty of our method is that these martingale inequalities are obtained as consequences of elementary deterministic counterparts. The latter have a natural interpretation in terms of robust hedging. Moreover, our deterministic…

We provide a general Doob-Meyer decomposition for $g$-supermartingale systems, which does not require any right-continuity on the system. In particular, it generalizes the Doob-Meyer decomposition of Mertens (1972) for classical supermartingales, as well as Peng's (1999) version for right-continuous $g$-supermartingale…

In this short note, we will strengthen the classic Doob's $L^p$ inequality for sub-martingale processes. Because this inequality is of fundamental importance to the theory of stochastic process, we believe this generalization will find many interesting applications.

In this paper, we study a type of reflected BSDE with a constraint and introduce a new kind of nonlinear expectation via BSDE with a constraint and prove the Doob-Meyer decomposition with respect to the super(sub)martingale introduced by this nonlinear expectation. We then apply the results to the pricing of American o…

In the paper, we introduce the notion of a local regular supermartingale relative to a convex set of equivalent measures and prove for it the necessary and sufficient conditions of optional Doob decomposition in the discrete case. This Theorem is a generalization of the famous Doob decomposition onto the case of superm…

The paper develops a computational method for efficient online filtering of diffusion processes.

Introduce a variance-weighted batch distribution for diverse sampling in diffusion models.

We extend diffusion models to function spaces and introduce a new method for sampling from posterior distributions.

New algorithm selects robust martingale for optimal stopping problems.

Adaptive denoising models adjust the number of steps based on noise level.

Unified approach to denoising Markov models for efficient sampling.

We extend Kyle's model to include stochastic liquidity and multiple assets.

ACSSM models irregular time series with continuous dynamics.

We build a general model for pricing defaultable claims. In addition to the usual absence of arbitrage assumption, we assume that one defaultable asset (at least) looses value when the default occurs. We prove that under this assumption, in some standard market filtrations, default times are totally inaccessible stoppi…

We consider filtration consistent nonlinear expectations in probability spaces satisfying only the usual conditions and separability. Under a domination assumption, we demonstrate that these nonlinear expectations can be expressed as the solutions to Backward Stochastic Differential Equations with Lipschitz continuous …

Paper defines saddle points in asymmetric Dynkin games using martingale theory.

We study quaternionic stochastic areas processes associated with Brownian motions on the quaternionic rank-one symmetric spaces $\mathbb{H}H^n$ and $\mathbb{H}P^n$. The characteristic functions of fixed-time marginals of these processes are computed and allows for the explicit description of their corresponding large-t…

In this paper, we first establish the reflected backward stochastic difference equations with finite state (FS-RBSDEs for short). Then we explore the Existence and Uniqueness Theorem as well as the Comparison Theorem by "one step" method. The connections between FS-RBSDEs and optimal stopping time problems are investig…

We analyse the structure of local martingale deflators projected on smaller filtrations. In a general continuous-path setting, we show that the local martingale part in the multiplicative Doob-Meyer decomposition of projected local martingale deflators are themselves local martingale deflators in the smaller informatio…

In this article, we follow the study of quadratic backward SDEs with jumps,that is to say for which the generator has quadratic growth in the variables (z; u), started in our accompanying paper [15]. Relying on the existence and uniqueness result of [15], we define the corresponding g-expectations and study some of the…

We propose a new definition for tameness within the model of security prices as Itô processes that is risk-aware. We give a new definition for arbitrage and characterize it. We then prove a theorem that can be seen as an extension of the second fundamental theorem of asset pricing, and a theorem for valuation of contin…

Paper develops a new probabilistic method for American options using entropy regularization.

A martingale framework for concept change detection based on testing data exchangeability was recently proposed (Ho, 2005). In this paper, we describe the proposed change-detection test based on the Doob's Maximal Inequality and show that it is an approximation of the sequential probability ratio test (SPRT). The relat…

We study a stochastic equation modeling the lay-down of fibers in the production process of nonwovens. The equation can be formulated as some manifold-valued Stratonovich stochastic differential equation. Especially, we study the long time behaviour of the stochastic process. Demanding mathematical difficulties arising…

We give an elementary proof of the celebrated Bichteler-Dellacherie Theorem which states that the class of stochastic processes $S$ allowing for a useful integration theory consists precisely of those processes which can be written in the form $S=M+A$, where $M$ is a local martingale and $A$ is a finite variation proce…

We present new extensions to a method for constructing several families of solvable one-dimensional time-homogeneous diffusions whose transition densities are obtainable in analytically closed-form. Our approach is based on a dual application of the so-called diffusion canonical transformation method that combines smoo…

Neural networks approximate superhedging prices in financial models.

The target of this paper is to establish the bid-ask pricing frame work for the American contingent claims against risky assets with G-asset price systems (see \cite{Chen2013b}) on the financial market under Knight uncertainty. First, we prove G-Dooby-Meyer decomposition for G-supermartingale. Furthermore, we consider …

Extends martingale Schrödinger bridge to arbitrary dimensions and characterizes it.

This paper generalizes neural transport learning for free energy estimation in arbitrary state spaces.

A new method uses deep learning for optimal stopping problems.

New proof shows local wealth condensation in economic models with biases.

Unified framework for inference in complex nonlinear processes.

Efficiently infers coupled hidden Markov models with noisy discrete observations.

In the paper, the martingales and super-martingales relative to a convex set of equivalent measures are systematically studied. The notion of local regular super-martingale relative to a convex set of equivalent measures is introduced and the necessary and sufficient conditions of the local regularity of it in the disc…

The present paper introduces a jump-diffusion extension of the classical diffusion default intensity model by means of subordination in the sense of Bochner. We start from the bi-variate process $(X,D)$ of a diffusion state variable $X$ driving default intensity and a default indicator process $D$ and time change it wi…

Novel framework for risk-sensitive reinforcement learning using martingale decomposition.

FHDMs achieve optimal convergence in spherically supported data.

SIGMA model improves graph matching across various applications.

Neural score matching improves high-dimensional causal inference by using neural networks for balancing scores.

Study dynamic matching in heterogeneous networks using ODE model.

Efficiently learns matching rewards in two-sided markets with matrix completion.

The strength of association between a pair of data vectors is represented by a nonnegative real number, called matching weight. For dimensionality reduction, we consider a linear transformation of data vectors, and define a matching error as the weighted sum of squared distances between transformed vectors with respect…