In this paper, we develop a new mathematical technique which allows us to express the joint distribution of a Markov process and its running maximum (or minimum) through the marginal distribution of the process itself. This technique is an extension of the classical reflection principle for Brownian motion, and it is o…
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48 results for “reflected process”
Study minimal solutions to a reflected process driven by jump processes.
problem Ruin time of interconnected insurance firms.
method Minimal strong solution to a particle system with a linear programming problem.
result Existence of a unique stopping time for the ruin process.
The paper studies large deviation principles for stochastic volatility models with reflection, focusing on binary barrier options and call prices.
problem Large deviation principles for stochastic volatility models with reflection.
method Sample path and small-noise large deviation principles for the log-price process.
result Asymptotic behavior of binary barrier options and call prices in the small-noise regime.
We study a doubly reflected backward stochastic differential equation (BSDE) with integrable parameters and the related Dynkin game. When the lower obstacle and the upper obstacle of the equation are completely separated, we construct a unique solution of the doubly reflected BSDE by pasting local solutions and…
The paper solves a control problem using reflections to track a benchmark process.
problem Optimal consumption with a benchmark process that grows over time.
method Introduced two auxiliary state processes with reflections to transform the problem into a more tractable form.
result Established the existence of a unique classical solution to the dual PDE.
Modified model prevents volatility from approaching zero.
problem Volatility in the Gatheral model can approach zero, making it statistically indistinguishable.
method Proposed a modified model with Skorokhod reflection to prevent volatility from approaching zero.
result The modified model prevents volatility from approaching zero, preserving the model's flexibility.
Bayesian RL enhances LLMs to reflectively explore and correct errors.
problem LLMs trained via RL lack reflective behaviors like rethinking and error correction.
method Bayesian RL framework that optimizes expected return under posterior distribution over Markov decision processes.
result BARL algorithm improves LLM performance in reasoning tasks.
The paper analyzes statistical guarantees for denoising reflected diffusion models.
problem The mismatch between theoretical design and implementation of diffusion models introduces issues in high-dimensional target data.
method The paper uses a reflected diffusion process as the driver of noise and establishes rates of convergence in total variation.
result The statistical guarantees for denoising reflected diffusion models match the minimax lower bound up to a polylogarithmic factor.
Well-posedness and penalization schemes for generalized BSDEs and reflected generalized BSDEsmath.PR
The paper tackles pricing vulnerable options via generalized BSDEs and penalization schemes.
problem Pricing options in a general hazard process setup.
method Establishes well-posedness and comparison theorems for generalized BSDEs and RBSDEs, studies penalization schemes.
result Well-posedness results and comparison theorems for generalized BSDEs and RBSDEs, extended penalization schemes.
Real-world measurement noise in applications like robotics is often correlated in time, but we typically assume i.i.d. Gaussian noise for filtering. We propose general Gaussian Processes as a non-parametric model for correlated measurement noise that is flexible enough to accurately reflect correlation in time, yet sim…
Coupling by reflection of diffusion processes via discrete approximation under a backward Ricci flowmath.PR
A coupling by reflection of a time-inhomogeneous diffusion process on a manifold are studied. The condition we assume is a natural time-inhomogeneous extension of lower Ricci curvature bounds. In particular, it includes the case of backward Ricci flow. As in time-homogeneous cases, our coupling provides a gradient esti…
The paper extends Merton's problem by adding benchmark tracking, finding optimal strategies.
problem Maximizing consumption utility with a trade-off against benchmark performance.
method Developed a convex duality theorem and derived optimal strategies for specific cases.
result Found optimal portfolio and consumption strategies for CRRA utility and geometric Brownian motion benchmarks.
This paper studies the bail-out optimal dividend problem with regime switching under the constraint that the cumulative dividend strategy is absolutely continuous. We confirm the optimality of the regime-modulated refraction-reflection strategy when the underlying risk model follows a general spectrally negative Markov…
This paper optimizes tracking portfolios in incomplete markets using reinforcement learning.
problem Optimizing tracking portfolios in incomplete markets with capital injection.
method Reinforcement learning approach for optimal control in reflected diffusion processes.
result Satisfactory performance of the q-learning algorithm in numerical examples.
Weak Convergence of Approximate reflection coupling and its Application to Non-convex Optimizationmath.PR
Paper proposes a weak approximation of reflection coupling for non-convex optimization.
problem Non-convex optimization problems with different drift terms.
method Proposes an approximate reflection coupling (ARC) for stochastic differential equations (SDEs).
result ARC converges weakly to the reflection coupling and can be applied to non-convex optimization.
Proposes a new method for constrained generative modeling using Langevin dynamics.
problem Challenges in satisfying underlying constraints with score-based generative models.
method Uses kinetic Langevin dynamics with specular reflection to model constraints.
result Demonstrates efficient numerical samplers with optimal convergence rates.
New algorithm enhances generative modeling for bounded domains.
problem Ad-hoc thresholding techniques for boundary enforcement in diffusion models.
method Reflected Schrödinger Bridge algorithm for entropy-regularized optimal transport.
result Generative modeling in diverse bounded domains with optimal transport properties.
FinVision uses LLM agents to predict stock markets by processing various financial data types.
problem Challenges in integrating diverse financial data for accurate stock market prediction.
method Multi-agent framework with LLMs specialized in different financial data types and a reflection module.
result The reflection module enhances decision-making capabilities for financial trading.
Study of multidimensional control problems with reflection controls.
problem Solving control problems with reflection controls in multidimensional settings.
method Gradient descent algorithm for polytope approximations, data-driven domain estimator, episodic learning algorithm.
result Data-driven solutions for unknown diffusion dynamics with sublinear regret.
This paper develops the first method for the exact simulation of reflected Brownian motion (RBM) with non-stationary drift and infinitesimal variance. The running time of generating exact samples of non-stationary RBM at any time is uniformly bounded by where is the average drift of…
Study no-arbitrage conditions in 1D diffusion markets with interest rates.
problem Determining no-arbitrage conditions in 1D diffusion markets with interest rates.
method Established deterministic criteria for no-arbitrage notions in terms of scale function and speed measure.
result Revealed various effects, e.g., NIP not excluded by reflecting boundaries.
We solve explicitly a two-dimensional singular control problem of finite fuel type for infinite time horizon. The problem stems from the optimal liquidation of an asset position in a financial market with multiplicative and transient price impact. Liquidity is stochastic in that the volume effect process, which determi…
We introduce a Bayesian approach to discovering patterns in structurally complex processes. The proposed method of Bayesian Structural Inference (BSI) relies on a set of candidate unifilar HMM (uHMM) topologies for inference of process structure from a data series. We employ a recently developed exact enumeration of to…
Reflected Diffusion Modelsstat.ML
Reflected Diffusion Models improve on score-based models by incorporating data constraints.
problem Numerical error in score-based models leads to unnatural samples.
method Reverses a reflected stochastic differential equation on data support, learning perturbed score function through generalized score matching loss.
result Improves sample quality and fidelity without architectural modifications.
We study a singular stochastic control problem faced by the owner of an insurance company that dynamically pays dividends and raises capital in the presence of the restriction that the surplus process must be above a given dividend payout barrier in order for dividend payments to be allowed. Bankruptcy occurs if the su…
We present a machine learning model for the analysis of randomly generated discrete signals, modeled as the points of an inhomogeneous, compound Poisson point process. Like the wavelet scattering transform introduced by Mallat, our construction is naturally invariant to translations and reflections, but it decouples th…
Based on a study of the coupling by reflection of diffusion processes, a new monotonicity in time of a time-dependent transportation cost between heat distribution is shown under Bakry-Emery's curvature-dimension condition on a Riemannian manifold. The cost function comes from the total variation between heat distribut…
Paper studies optimal tracking portfolio in mean field game of large fund competition.
problem Optimal tracking portfolio in large fund competition with relative performance benchmark.
method Formulated mean field game problem, established existence of mean field equilibrium using PDE approach, constructed approximate Nash equilibrium.
result Existence of mean field equilibrium and consistency condition verified.
We study optimal buying and selling strategies in target zone models. In these models the price is modeled by a diffusion process which is reflected at one or more barriers. Such models arise for example when a currency exchange rate is kept above a certain threshold due to central bank intervention. We consider the op…
SEP framework teaches LLMs to generate explainable stock predictions.
problem Challenging task of generating human-readable explanations for stock predictions.
method Self-reflective agent and Proximal Policy Optimization (PPO) for autonomous learning.
result Fine-tuned LLM outperforms traditional methods in prediction accuracy and Matthews correlation coefficient.
Consider observing a collection of discrete events within a network that reflect how network nodes influence one another. Such data are common in spike trains recorded from biological neural networks, interactions within a social network, and a variety of other settings. Data of this form may be modeled as self-excitin…
In this paper we study Backward Stochastic Differential Equations with two reflecting right continuous with left limits obstacles (or barriers) when the noise is given by Brownian motion and a Poisson random measure mutually independent. The jumps of the obstacle processes could be either predictable or inaccessible. W…
CNNs improve InSAR coherence classification.
problem Improving demarcation of InSAR imagery regions based on coherence.
method Convolutional Neural Networks (CNNs) for preprocessing and classification.
result CNNs reduce misclassifications in incoherent regions and outperform established methods.
A discrete subgroup of the group of isometries of the hyperbolic space is called reflective if up to a finite index it is generated by reflections in hyperplanes. The main result of this paper is a complete classification of the reflective (and quasi-reflective) subgroups among the Bianchi groups and their extensions.
New method produces reflections with nonseparating fixed points.
problem Constructing hyperbolic manifolds with reflective symmetries.
method Standard method for constructing closed hyperbolic manifolds.
result Fixed point sets of reflections are nonseparating.
Survey explores interactions between four conformal dynamics branches.
problem Understanding complex dynamics through different mathematical concepts.
method Examples and general results with technical tools.
result Dynamical relations between Schwarz reflection parameter spaces and anti-rational maps/ reflection groups.
One reflection suffices for orthogonal weights, reducing GPU usage.
problem Efficiently computing orthogonal weight matrices without high GPU utilization.
method Use an auxiliary neural network to compute one reflection instead of many.
result One reflection is sufficient for orthogonal weights, improving GPU utilization.
Study optimal consumption with relaxed benchmarks and drawdown constraints.
problem Optimal consumption under relaxed benchmark tracking and consumption drawdown constraint.
method Transformed stochastic control problem into regular control problem with state-control constraints, then solved using dual transform and optimal consumption behavior.
result Closed-form solution for optimal investment and consumption in feedback form.
On optimal joint reflective and refractive dividend strategies in spectrally positive Lévy modelsmath.OC
The expected present value of dividends is one of the classical stability criteria in actuarial risk theory. In this context, numerous papers considered threshold (refractive) and barrier (reflective) dividend strategies. These were shown to be optimal in a number of different contexts for bounded and unbounded payout …
Minimal surfaces in 3-sphere created by reflections from polygons, with new examples based on pentagons.
problem Constructing minimal surfaces in 3-sphere using reflections.
method Minimal -gon solves free boundary problem; curvature lines combinatorics investigated.
result New examples of minimal reflection surfaces based on pentagons.
We analyze exponential integrability properties of the Cox-Ingersoll-Ross (CIR) process and its Euler discretizations with various types of truncation and reflection at 0. These properties play a key role in establishing the finiteness of moments and the strong convergence of numerical approximations for a class of sto…
Study thin hyperbolic reflection groups and their properties.
problem Characterize and enumerate thin hyperbolic reflection groups.
method Analyze Zariski dense subgroups of hyperbolic isometries, apply Vinberg algorithm.
result All thin hyperbolic reflection groups are enumerable.
We consider the optimal stopping problem with non-linear -expectation (induced by a BSDE) without making any regularity assumptions on the reward process . and with general filtration. We show that the value family can be aggregated by an optional process . We characterize the process as the $\mathcal{E}^f…
Proposes a method to align Hawkes processes across different event spaces.
problem Aligning Hawkes processes in multiple event spaces.
method Fused Gromov-Wasserstein alignment for Hawkes processes.
result The method effectively aligns Hawkes processes and their event types.
The latter author, together with collaborators, proposed a numerical scheme to calculate the price of barrier options. The scheme is based on a symmetrization of diffusion process. The present paper aims to give a mathematical credit to the use of the numerical scheme for Heston or SABR type stochastic volatility model…
Minimal surfaces reflect across spheres, proving annulus uniqueness.
problem Uniqueness of free boundary minimal annuli in balls.
method Reflection principle applied to minimal surfaces meeting spheres at 90 degrees.
result Every embedded free boundary minimal annulus in a ball is the critical catenoid.
Hausdorff reflection keeps space shape intact.
problem Preserving shape type in spaces.
method Hausdorff reflection method.
result Hausdorff reflection preserves shape type.
On weakly reflective submanifolds in compact isotropy irreducible Riemannian homogeneous spacesmath.DG
Study extends reflective submanifold theory to compact homogeneous spaces.
problem Characterize reflective submanifolds in compact isotropy irreducible spaces.
method Extend previous results to infinite-dimensional Hilbert spaces.
result Inverse image of reflective submanifolds is also reflective.