In this note, we study the ultimate ruin probabilities of a real-valued L{é}vy process X with light-tailed negative jumps. It is well-known that, for such L{é}vy processes, the probability of ruin decreases as an exponential function with a rate given by the root of the Laplace exponent, when the initial value goes to …
Study on ruin probability with investment in risky assets modeled as semimartingales.
problem Analyzing ruin probability in a business process with investment in risky assets.
method Investigates ruin probability with investment in a Lévy process and semimartingale return, deriving upper bounds and conditions for ruin.
result Upper bounds on ruin probabilities decrease as a power function with increasing initial capital, and these bounds are asymptotically optimal.
This paper presents generalized momentum mappings for covariant Hamiltonian field theories. The new momentum mappings arise from a generalization of symplectic geometry to L V Y L_VY L V Y , the bundle of vertically adapted linear frames over the bundle of field configurations Y Y Y . Specifically, the generalized field momentum obs…
Constructs supermartingale couplings with full marginals constraints.
problem Optimal transport for supermartingale couplings with multiple marginals.
method Markovian iteration of one-period optimal supermartingale couplings.
result Explicit construction of supermartingale processes solving optimal transport problem.
The paper optimizes utility for switching models using Lévy processes.
problem Maximizing HARA utilities in Lévy switching models.
method Dual method, f-divergence minimal martingale measures, Hellinger and Kulback-Leibler processes.
result Expressions for optimal strategies and maximal expected utilities.
Let M M M be a manifold, V V V be a vector field on M M M , and B B B be a Banach space. For any fixed function f : M → B f:M\rightarrow B f : M → B and any fixed complex number λ λ λ , we study Hyers-Ulam stability of the global differential equation V y = λ y + f Vy=λy+f V y = λ y + f .
Modeling financial markets with a novel order flow model.
problem Inconsistent parameter values from long-range memory estimators.
method Tsallis q-exponential distribution for limit order cancellation times.
result Improved accuracy in predicting financial market dynamics.
The paper provides a representation for dynamic risk measures and capital allocations.
problem Representation of dynamic risk measures and capital allocations under Itô-Lévy model.
method Representation theorem for dynamic capital allocation derived from BSDEs with quadratic-exponential growth.
result Derivation of a capital allocation representation for dynamic entropic risk measure and static coherent risk measure.
The Wiener-Hopf factorization is obtained in closed form for a phase type approximation to the CGMY Lévy process. This allows, for the approximation, exact computation of first passage times to barrier levels via Laplace transform inversion. Calibration of the CGMY model to market option prices defines the risk neutral…
We introduce a class of interest rate models, called the α α α -CIR model, which gives a natural extension of the standard CIR model by adopting the α α α -stable L{é}vy process and preserving the branching property. This model allows to describe in a unified and parsimonious way several recent observations on the sovereign …
We prove that a compact stratied space satises the Riemannian curvature-dimension condition RCD(K, N) if and only if its Ricci tensor is bounded below by K ∈ \in ∈ R on the regular set, the cone angle along the stratum of codimension two is smaller than or equal to 2 π π π and its dimension is at most equal to N. This gives…
This paper sets baselines for reading comprehension benchmarks, finding simple models often perform well.
problem Understanding the difficulty of popular reading comprehension benchmarks.
method Established baselines for bAbI, SQuAD, CBT, CNN, and Who-did-What datasets.
result Simple models often outperform complex models on many benchmarks.
The distribution of trade sizes and trading volumes are investigated based on the limit order book data of 22 liquid Chinese stocks listed on the Shenzhen Stock Exchange in the whole year 2003. We observe that the size distribution of trades for individual stocks exhibits jumps, which is caused by the number preference…
MT-VAE learns motion transitions for generating diverse future motions.
problem Learning long-term human motion sequences with transitions.
method Jointly learns motion mode embeddings and transitions using Variational Auto-Encoders.
result Generates multiple plausible future motion sequences from input.
Introduces Motion Programs for better video analysis of human motion.
problem Current video analysis focuses on raw pixels or keypoints, missing higher-level motion primitives.
method Introduces Motion Programs as a neuro-symbolic representation of motions as a composition of high-level primitives.
result Motion Programs accurately describe diverse human motions and improve downstream tasks.
Study motion planning for points avoiding obstacles in a plane.
problem Avoiding collisions for multiple points in a plane with unknown obstacles.
method Algebraic and topological tools for motion planning.
result New topological complexity for planar motion planning.
Paper introduces new motion synthesis model using normalizing flows.
problem Data-driven motion synthesis with probabilistic and controllable models.
method Probabilistic, generative, autoregressive model using normalizing flows and LSTMs.
result Randomly sampled motion from the model outperforms task-agnostic baselines.
Programmatic Motion Concepts learn human actions from paired videos.
problem Learning motion concepts from paired video and action sequences.
method Semi-supervised learning architecture for hierarchical motion representation.
result Outperforms established baselines, especially in small data settings.
We provide an empirical investigation aimed at uncovering the statistical properties of intricate stock trading networks based on the order flow data of a highly liquid stock (Shenzhen Development Bank) listed on Shenzhen Stock Exchange during the whole year of 2003. By reconstructing the limit order book, we can extra…
Unified framework for human motion generation on Riemannian manifolds.
problem Learning valid human motion in Euclidean spaces.
method Riemannian Motion Generation (RMG) on product manifolds, Riemannian flow matching.
result Achieves state-of-the-art FID (0.043) on HumanML3D and surpasses strong baselines on MotionMillion.
Study on determinants of unitary Brownian motion and their asymptotic laws.
problem Understanding determinants of unitary Brownian motion and their behavior over time.
method Using Stiefel fibration and skew-product decomposition of the Stiefel Brownian motion.
result Prove asymptotic laws for determinants of block entries of unitary Brownian motion.
New framework predicts diverse, contextually plausible 3D human motions.
problem Predicting multiple plausible future 3D poses given observed poses.
method Developed a new variational framework that conditions latent variable on past observation to encourage relevant information.
result Our approach generates motions of higher quality and preserves contextual information.
Neural network predicts vessel motions with high accuracy.
problem Real-time prediction of heave and surge motions for improved performance and safety.
method Developed an LSTM-based machine learning model trained on measured waves and motion data.
result The model predicts vessel motions up to 46.5 seconds into the future with an average accuracy of 90%.
Study refracted skew Brownian motion, find densities and asymptotics.
problem Modeling and analyzing refracted skew Brownian motion.
method Perturbation approach to find potential densities, transition density, and asymptotic behaviors.
result Expressions and asymptotic behaviors of refracted skew Brownian motion.
Study fractal dimension for motion without crossing a subset.
problem Fractal dimension of a subset X in R^n for motion without crossing.
method Analyzes fractal dimension of subset X in R^n.
result Determines conditions for motion without crossing a subset.
Let E E E be a closed set in the Riemann sphere C ^ \widehat{\mathbb{C}} C . We consider a holomorphic motion φ φ φ of E E E over a complex manifold M M M , that is, a holomorphic family of injections on E E E parametrized by M M M . It is known that if M M M is the unit disk Δ Δ Δ in the complex plane, then any holomorphic motion of E E E ove…
Neural network estimates rigid motion in stroke imaging to improve image quality.
problem Rigid patient motion during C-arm CBCT imaging reduces image quality.
method Neural network trained to regress reprojection error based on image information.
result Neural network outperforms entropy-based method in motion estimation.
Study cohomological equation for robotic screw motions on SE(3).
problem Understanding obstruction phenomena in robotic rigid-body motion.
method Combining Fourier analysis and Peter-Weyl theory, reduce to finite-dimensional linear transport systems.
result Explicit screw motion illustrates resonance conditions and finite-dimensional obstructions.
New approach for obstacle avoidance in robotics using learned representations.
problem Challenges in sensor-based motion planning for new and dynamic environments.
method Proposes a new obstacle representation using PointNet architecture trained jointly with policies for obstacle avoidance.
result Significant improvements in accuracy and efficiency compared to state of the art.
The paper presents a method to reduce arm motion complexity for prosthetics and robotics.
problem Reducing the complexity of human arm motions for robotic and prosthetic control.
method Data-driven techniques including DTW, DBA, Ward's distance, batch-DTW, and fPCA.
result Representative motion clusters and averages for different arm DOF levels.
Paper defines multi-dimensional fractional Brownian motion under volatility uncertainty.
problem Volatility uncertainty in fractional Brownian motion.
method Definition and study of multi-dimensional fractional Brownian motion (G-fBm) with Hurst index.
result First results on stochastic calculus for G-fBm with Hurst index > 0.5.
Paper introduces a new method for generating diverse human motion predictions.
problem Stochastic human motion prediction with limited flexibility.
method Stochastically combines root variations with previous pose information in a recurrent network.
result Model generates more diverse motion sequences than existing techniques.
Researchers calculate the Laplace transform of a geometric Brownian motion integral.
problem Calculating the Laplace transform of a specific integral functional of geometric Brownian motion.
method Analytical calculation of the Laplace transform of the cumulative distribution and probability density functions.
result The Laplace transform of the integral functional of geometric Brownian motion is derived.
Researchers created a continuous Markov martingale that mimics Brownian motion but lacks the strong Markov property.
problem Constructing a continuous Markov martingale with Brownian marginals that misses the strong Markov property.
method Developed a new approach to create a continuous Markov martingale that differs from Brownian motion in terms of the strong Markov property.
result A continuous Markov martingale with Brownian marginals that lacks the strong Markov property was successfully constructed.
We consider n n n -dimensional discrete motions such that any two neighbouring positions correspond in a pure rotation ("rotating motions"). In the Study quadric model of Euclidean displacements these motions correspond to quadrilateral nets with edges contained in the Study quadric ("rotation nets"). The main focus of ou…
Improved vehicle motion prediction with uncertainty estimation.
problem Robust motion prediction for autonomous vehicles, especially under distributional shift.
method Presented an approach significantly improving the benchmark and taking 2nd place on the leaderboard.
result Significantly improved motion prediction and uncertainty measurement.
A framework for computing holonomy groups of hybrid systems to achieve forward motion.
problem Achieving forward motion from periodic leg motion.
method Developing a framework for computing holonomy groups of hybrid systems.
result Computing holonomy groups of hybrid systems to achieve non-zero net motion.
The paper explores representations of graph manifolds to Seifert motion groups.
problem Existence of faithful representations of graph manifolds to Seifert motion groups.
method Discussion and proof of non-existence of certain representations.
result Graph manifolds can have virtually no faithful representations to the Seifert motion group.
Geodesic walks converge to Brownian motion on Finsler manifolds.
problem Understanding random walks on Finsler manifolds.
method Analyzing convergence of geodesic random walks to diffusion processes.
result The Brownian motion on a Riemannian metric is a key result.
MPNet uses neural networks for efficient motion planning.
problem Exponential increase in computational complexity with motion planning problem dimensionality.
method MPNet encodes workspaces from point cloud measurements and generates collision-free paths.
result MPNet is computationally efficient and generalizes to unseen environments.
Study homotopy motions of surfaces in 3-manifolds.
problem Understanding the behavior of surfaces under continuous deformations in 3-manifolds.
method Introduce and study homotopy motions of surfaces in closed orientable 3-manifolds.
result Systematic study of homotopy motions of surfaces in 3-manifolds.
The paper proposes a model to forecast traffic motion from sensor data.
problem Accurately predicting traffic motion for safe vehicle maneuvers.
method Implicit latent variable model using interaction graphs and graph neural networks.
result Achieves state-of-the-art motion forecasting and interaction understanding.
New SDEs use G G G -Brownian motion, extending mean-field models.
problem Extending mean-field models to new types of stochastic processes.
method Introduced G G G -SDEs with coefficients dependent on current state and solution as random variable. result Validated new SDE framework for complex stochastic systems.
This paper shows that explicitly learning motion improves reinforcement learning in dynamic environments.
problem Learning controllers for dynamic environments without explicit motion representation.
method Explicitly learning motion representation using image difference or temporal stacks of frames.
result Explicit motion learning improves the quality of learned controllers in dynamic scenarios.
A new model captures option price dynamics using sub-fractional Brownian motion.
problem Capturing the complex price dynamics of financial options.
method Developed a CEV model driven by a mixed sub-fractional Brownian motion.
result Empirical tests show the model effectively captures option price dynamics.
New model uses generalized fractional Brownian motion for stock price prediction.
problem Traditional models fail to accurately predict stock price fluctuations.
method Introduces generalized fractional Brownian motion as a new stochastic process for price modeling.
result Validates the new model for option pricing and risk assessment.
Proposes using Dynamic Mode Decomposition with delays for short-term human motion anticipation.
problem Lack of interpretability and explainability in neural network-based motion anticipation methods.
method Dynamic Mode Decomposition with delays for motion representation and prediction.
result Anticipation errors comparable or better than recurrent neural networks for very short times.
Equations for minimal surfaces from rigid motions in high dimensions.
problem Finding minimal surfaces from rigid motions in R N \mathbb{R}^N R N . method Derives equations for minimal surfaces using rigid motions in R N \mathbb{R}^N R N . result Equations for minimal surfaces in R N \mathbb{R}^N R N .