We solve a version of the optimal trade execution problem when the mid asset price follows a displaced diffusion. Optimal strategies in the adapted class under various risk criteria, namely value-at-risk, expected shortfall and a new criterion called "squared asset expectation" (SAE), related to a version of the cost v…
Efficiently calibrates Libor Market Model with SV-DD using Edgeworth expansions.
problem Calibrating the Libor Market Model with Stochastic Volatility and Displaced Diffusion.
method Combining Edgeworth and Gram-Charlier expansions with moments up to fourth order.
result 98% reduction in computational time for DD-SV-LMM calibration.
The paper shows subexponential growth and displacement bounds for random walks on graphs with bounded degrees and non-negative curvature.
problem Analyzing subexponential growth and displacement bounds for random walks on graphs with bounded degrees and non-negative curvature.
method Proving bounds on the continuous-time random walk displacement and log-volume growth using Ollivier--Ricci curvature.
result The paper establishes subexponential growth and displacement bounds for random walks on graphs with bounded degrees and non-negative curvature.
We investigate the m-relative entropy, which stems from the Bregman divergence, on weighted Riemannian and Finsler manifolds. We prove that the displacement K-convexity of the m-relative entropy is equivalent to the combination of the nonnegativity of the weighted Ricci curvature and the K-convexity of the weig…
We derive the joint density of a Skew Brownian motion, its last visit to the origin, local and occupation times. The result is applied to option pricing in a two valued local volatility model and in a displaced diffusion model with constrained volatility.
We generalize the reaction-diffusion model A + B -> 0 in order to study the impact of an excess of A (or B) at the reaction front. We provide an exact solution of the model, which shows that linear response breaks down: the average displacement of the reaction front grows as the square-root of the imbalance. We argue t…
Non-negative curvature affects Markov chains' mixing and expansion properties.
problem Understanding the behavior of Markov chains with non-negative curvature.
method Analyzing conductance, displacement, and cutoff phenomenon in sparse Markov chains.
result Non-negatively curved Markov chains exhibit specific, non-standard behavior in terms of mixing and expansion.
Graphs with bounded degrees and non-negative Ollivier-Ricci curvature have subexponential growth and diffusive random walk.
problem Understanding geometric properties of graphs with non-negative Ollivier-Ricci curvature.
method Analyzing the geometric properties of graphs with non-negative Ollivier-Ricci curvature, proving subexponential growth and diffusive random walk.
result For graphs with bounded degrees and non-negative Ollivier-Ricci curvature, the average log-volume growth and random walk displacement are subexponential.
Unified approach unites GANs and diffusion models using particle methods.
problem Combining GANs and diffusion models for generative tasks.
method Proposes a unified framework where generator training is seen as a generalization of particle models.
result Demonstrates that GANs and diffusion models can be integrated within a unified framework.
Flow Matching enables robust training of CNFs with various probability paths.
problem Training Continuous Normalizing Flows (CNFs) at large scales.
method Flow Matching (FM) is a simulation-free approach for training CNFs by regressing vector fields of conditional probability paths.
result Flow Matching with diffusion paths yields more robust and stable training compared to diffusion-based methods.
We study a Markov-Functional (MF) interest-rate model with Uncertain Volatility Displaced Diffusion (UVDD) digital mapping, which is consistent with the volatility-smile phenomenon observed in the option market. We first check the impact of pricing Bermudan swaptions by the model. Next, we also investigate the future s…
Survey of diffusion and optimal transport methods in machine learning.
problem Design and analysis of time-evolving probability distributions in machine learning.
method Switch from Eulerian to Lagrangian representation through vector fields.
result Both diffusion methods and optimal transport offer computational advantages.
In this paper we prove the Conley conjecture and the almost existence theorem in a neighborhood of a closed nowhere coisotropic submanifold under certain natural assumptions on the ambient symplectic manifold. Essential to the proofs is a displacement principle for such submanifolds. Namely, we show that a topologicall…
New displacement technique vanishes bounded cohomology in all degrees.
problem Vanishing of bounded cohomology in all positive degrees and dual separable coefficients.
method Introducing the property of commuting cyclic conjugates as a new displacement technique.
result Vanishes bounded cohomology in all positive degrees and all dual separable coefficients.
PIE-PINN estimates elastic properties from noisy, low-res displacement data.
problem Estimating heterogeneous elastic properties from low-resolution, noisy data.
method Probabilistic Physics-Informed Neural Network (PIE-PINN) framework combining B-spline and hierarchical scale model.
result Robust estimation of Young's modulus and Poisson's ratio from noisy, low-resolution displacement data.
This study finds similarities between currency exchange dynamics and supercooled systems.
problem Understanding the dynamics of currency exchange markets.
method Comparing EURUSD price fluctuations to colloidal dynamics and using models for arrested physical systems.
result EURUSD price fluctuations exhibit two-step dynamics similar to supercooled systems.
Nonnegative sectional curvature linked to matrix displacement convexity.
problem Nonnegative sectional curvature in Riemannian manifolds.
method Matrix displacement convexity as a criterion for nonnegative sectional curvature.
result Entropy functional matrix displacement convexity implies nonnegative sectional curvature.
Stock price changes occur through transactions, just as diffusion in physical systems occurs through molecular collisions. We systematically explore this analogy and quantify the relation between trading activity - measured by the number of transactions NΔt - and the price change GΔt, for a given stock, over …
We define the symplectic displacement energy of a non-empty subset of a compact symplectic manifold as the infimum of the Hofer-like norm [5] of symplectic diffeomorphisms that displace the set. We show that this energy (like the usual displacement energy defined using Hamiltonian diffeomorphisms) is a strictly positiv…
New method learns compressed transforms with flexible displacement operators.
problem Efficiently representing and learning shift-invariant patterns in neural networks.
method Explicitly learns over displacement operators and low-rank components in LDR matrices.
result Reduces sample complexity and improves model accuracy with fewer parameters.
The Homogeneity Conjecture explores if constant displacement isometries imply homogeneous spaces.
problem Whether constant displacement isometries on a manifold imply its homogeneity.
method Survey and verification of cases, including new results.
result New results and open problems suggested.
This paper optimizes functions of probability measures using particle gradient descent for displacement convex functions.
problem Optimizing functions of probability measures with displacement convex properties.
method Particle gradient descent applied to displacement convex functions with theoretical guarantees.
result Finite number of particles and computations are sufficient to find optimal solutions for displacement convex functions.
Minimal displacement set in weakly systolic complexes is systolic and embeds isometrically.
problem Structure of minimal displacement set in weakly systolic complexes.
method Investigation of minimal displacement set properties and embeddings.
result Minimal displacement set is systolic and embeds isometrically into the complex.
We discuss in this article a property of action of groups by isometries called "well displacing". An action is said to be well displacing, if the displacement function is equivalent to the the displacement function for the action on the Cayley graph. We relate this property with the fact that orbit maps are quasi-isome…
Alexandrov spaces with non-negative curvature are characterized by the matrix displacement convexity of an entropy tensor.
problem Characterizing non-negative curvature in Alexandrov spaces
method Constructing a parallel trivialization of the entropy tensor
result The entropy tensor is matrix displacement convex on Alexandrov spaces
In this article we study the Hamiltonian non-displaceability of Gauss images of isoparametric hypersurfaces in the spheres as Lagrangian submanifolds embedded in complex hyperquadrics.
New curvature measure for optimal transport with specific cost function.
problem Optimal transport with specific cost function.
method Proposed generalized curvature measure.
result Non-negativity of the generalized curvature implies displacement convexity.
The paper proposes a model to learn motion perception in V1 using vector and matrix representations.
problem Motion perception in primary visual cortex (V1).
method Coupling vector representations of local contents and matrix representations of local pixel displacements.
result The model can learn Gabor-like filter pairs and infer local motions.
Training models to prefer certain responses can unintentionally shift probability to harmful ones.
problem Likelihood displacement in DPO models, leading to unintended unalignment.
method Characterized and mitigated likelihood displacement using CHES score.
result Training models to prefer certain responses can unintentionally shift probability mass to harmful responses.
Sparse elasticity reconstruction from local displacements reduces error.
problem Reconstructing elasticity from limited data.
method Sparse elasticity reconstruction theory, local clustering, alternating optimization.
result Higher spatial resolution elasticity distribution estimation.
We prove that the displacement energy of a stable coisotropic submanifold is bounded away from zero if the ambient symplectic manifold is closed, rational and satisfies a mild topological condition.
The paper suggests asset prices follow physical laws, allowing for accurate price movement forecasts.
problem Predicting extreme price movements in financial markets.
method Modeling asset price dynamics as a harmonic oscillator and applying the principle of stationary action.
result The theory can make accurate forecasts of price movements during market crashes and specific price displacements at other times.
The null energy condition is characterized via convexity of entropy in Lorentzian manifolds.
problem Characterizing the null energy condition in Lorentzian manifolds.
method Characterization via convexity of the relative entropy along displacement interpolations on null hypersurfaces.
result The null energy condition is characterized in terms of convexity of the relative entropy.
Derives sub-Riemannian Ricci curvature for various manifolds.
problem Calculating Ricci curvature in sub-Riemannian geometry.
method Generalized Gamma z calculus and z--Bochner's formula. result Analytical bounds for sub-Riemannian curvature dimension and log-Sobolev inequalities.
Proves inequality for Fuchsian groups, improving surface geometry.
problem Displacement of generators in free Fuchsian groups.
method Analyzes displacement inequalities for Fuchsian groups.
result Quantitative results on hyperbolic surface geometry.
LDR neural networks reduce space and complexity with high accuracy.
problem Reducing space and computational complexity in large-scale neural networks.
method Formal study of LDR matrices, proving approximation property, error bounds, and proposing training algorithm.
result LDR neural networks achieve high accuracy with significant reduction in space and computational complexity.
Study automorphism groups of quandles up to order 10.
problem Understanding automorphism groups of quandles of various orders.
method Enumerated and computed automorphism groups and displacement groups of quandles up to order 10.
result Computed automorphism groups and displacement groups for all quandles up to order 10.
We generalize Lagrangian Floer cohomology to sequences of Lagrangian correspondences. For sequences related by the geometric composition of Lagrangian correspondences we establish an isomorphism of the Floer cohomologies. We give applications to calculations of Floer cohomology, displaceability of Lagrangian correspond…
In this paper we make the first steps towards developing a theory of intersections of coisotropic submanifolds, similar to that for Lagrangian submanifolds. For coisotropic submanifolds satisfying a certain stability requirement we establish persistence of coisotropic intersections under Hamiltonian diffeomorphisms, ak…
Study uses barcode theory to bound displacement energy of Legendrian submanifolds.
problem Bounding displacement energy for Legendrian submanifolds.
method Applies barcodes of persistent homology to Chekanov-Eliashberg algebra, linearizing only below a certain action level.
result Shows Legendrians that admit augmentations cannot be C0-approximated by stabilized Legendrians. Paper derives formulas for surface variations in shell theory.
problem Deriving first variation formulas for surfaces in thin shell theory.
method Using strain-displacement relations from thin shell theory.
result Provides formulas for linear Weingarten surfaces as stationary points.
In this paper we give an explicit description of the bounded displacement isometries of a class of spaces that includes the Riemannian nilmanifolds. The class of spaces consists of metric spaces (and thus includes Finsler manifolds) on which an exponential solvable Lie group acts transitively by isometries. The bounded…
We construct using Lefschetz fibrations a large family of contact manifolds with the following properties: Any bounding contact embedding into an exact symplectic manifold satisfying a mild topological assumption is non-displaceable and generically has infinitely many leaf-wise intersection points. Moreover, any Stein …
Proportional transaction costs present difficult theoretical problems in trading algorithm design, on account of their lack of analytical tractability. The author derives a solution of DT-NT-DT form for an arbitrary model in which the the traded asset has diffusive dynamics described by one or more stochastic risk fact…
We discuss modelling of SPX and DAX index option prices using the Shifted Log-Normal (SLN) model, (also known as Displaced Diffusion), and the SABR model. We found out that for SPX options, an example of strongly skewed option prices, SLN can produce a quite accurate fit. Moreover, for both types of index options, the …
Dehn's Lemma for loops in 3-manifolds.
problem Dehn's Lemma for loops in 3-manifolds.
method Null-homotopic curve in a 3-manifold M can be displaced by a height function in a collar of the boundary.
result An immersed closed curve in the boundary of a 3-manifold can be displaced to a simple closed curve bounding a disk in the 3-manifold.
Study of rigid body displacements in a projective space over dual numbers with geometric interpretations.
problem Understanding rigid body displacements in a novel geometric space.
method Projective differential geometry over the ring of dual numbers.
result Existence of non-straight curves with multiple osculating tangents.
Study uses satellite data to predict tailings dam collapse risk.
problem Detecting early signs of tailings dam instability.
method Spectral analysis of satellite InSAR displacement time series data.
result Algorithm detects risk milestones up to 5 months before dam collapse.