A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Improved Hawkes model captures price dynamics and volatility.
We study an optimal investment problem under default risk where related information such as loss or recovery at default is considered as an exogenous random mark added at default time. Two types of agents who have different levels of information are considered. We first make precise the insider's information flow by us…
The purpose of this paper is to design an algorithm for the computation of the counterparty risk which is competitive in regards of a brute force "Monte-Carlo of Monte-Carlo" method (with nested simulations). This is achieved using marked branching diffusions describing a Galton-Watson random tree. Such an algorithm le…
Motivated by the prediction of cell loads in cellular networks, we formulate the following new, fundamental problem of statistical learning of geometric marks of point processes: An unknown marking function, depending on the geometry of point patterns, produces characteristics (marks) of the points. One aims at learnin…
We show that the largest subsurface projection distance between a marking and its image under the nth step of a random walk grows logarithmically in n, with probability approaching 1 as n tends to infinity. Our setup is general and also applies to (relatively) hyperbolic groups and to . We then use t…
We apply the formalism of the continuous time random walk to the study of financial data. The entire distribution of prices can be obtained once two auxiliary densities are known. These are the probability densities for the pausing time between successive jumps and the corresponding probability density for the magnitud…
Modeling intraday electricity prices with a Hawkes process.
We present a marked analogue of Carter and Saito's movie theorem. Our definition of marking was chosen to coincide with the markings that arise in link Floer homology. In order to deal with complications arising from certain isotopies, we define three equivalence relations for marked surfaces and work over an equivalen…
We are now witnessing the increasing availability of event stream data, i.e., a sequence of events with each event typically being denoted by the time it occurs and its mark information (e.g., event type). A fundamental problem is to model and predict such kind of marked temporal dynamics, i.e., when the next event wil…
New model captures time and mark inter-dependence in TPPs.
Study applies Hawkes volatility to mid-price process for real-time risk management.
We develop a probabilistic framework for sequential random projection.
Algorithms compute length spectra of torus graphs efficiently.
A marked graph diagram is a link diagram possibly with marked -valent vertices. S. J. Lomonaco, Jr. and K. Yoshikawa introduced a method of representing surface-links by marked graph diagrams. Specially, K. Yoshikawa gave local moves on marked graph diagrams, nowadays called Yoshikawa moves. It is now known that two…
Dynamic risk measures are defined using BSDEs in a filtration enlargement setting.
Methodology for estimating marked Hawkes processes with neural networks.
Study approximate marked length spectrum rigidity in non-positively curved groups.
We classify GL(2,R) invariant point markings over components of strata of Abelian differentials. Such point markings exist only when the component is hyperelliptic and arise from marking Weierstrass points or two points exchanged by the hyperelliptic involution. We show that these point markings can be used to determin…
We use Fox calculus to assign a marked polytope to a `nice' group presentation with two generators and one relator. Relating the marked vertices to Novikov-Sikorav homology we show that they determine the Bieri-Neumann-Strebel invariant of the group. Furthermore we show that in many cases the marked polytope is an inva…
Quantum duality map extended to general marked surfaces and its compatibility with skein algebras proven.
In this paper, we construct the moduli space of marked oper structures on a closed, oriented smooth surface of negative Euler characteristic as a holomorphic fiber bundle over Teichmüller space. We prove that the holonomy map from the space of marked oper structures to the moduli space of reductive flat bundles is a ho…
Paper shows non-arithmetic surface with unique geometric property.
In this paper we study the skein algebras of marked surfaces and the skein modules of marked 3-manifolds. Muller showed that skein algebras of totally marked surfaces may be embedded in easy to study algebras known as quantum tori. We first extend Muller's result to permit marked surfaces with unmarked boundary compone…
A graph helps understand Artin groups better.
In all dimensions, we prove that the marked length spectrum of a Riemannian manifold with Anosov geodesic flow and non-positive curvature locally determines the metric in the sense that two close enough metrics with the same marked length spectrum are isometric. In addition, we provide a completely new stabilit…
RR-GCN uses random transformations instead of learned weights for node embeddings.
Survey of stated skein modules/algebras of 3-manifolds/surfaces.
We show that all GL(2,R) equivariant point markings over orbit closures of translation surfaces arise from branched covering constructions and periodic points, completely classify such point markings over strata of quadratic differentials, and give applications to the finite blocking problem.
It is well known that surface-links in 4-space can be presented by diagrams on the plane of 4-valent spatial graphs with makers on the vertices, called marked graph diagrams. In this paper we extend the method of presenting surface-links by marked graph diagrams to presenting immersed surface-links. We also give some m…
Develops quasi-likelihood analysis for marked point processes and applies it to Hawkes processes.
The paper extends intensity models for limit order books using marked point processes.
We prove that the classical set of moves for standard spines of 3-manifolds (i.e. the MP-move and the V-move) does not suffice to relate to each other any two standard skeleta of a 3-manifold with marked boundary. We also describe a condition on the 3-manifold with marked boundary that tells whether the generalised set…
Study of infinite type surfaces' mapping class groups via hyperbolic structures.
Closed manifolds with close marked spectra are approximately isometric.
By using the cohomology theory of quandles, quandle cocycle invariants and shadow quandle cocycle invariants are defined for oriented links and surface-links via broken surface diagrams. By using symmetric quandles, symmetric quandle cocycle invariants are also defined for unoriented links and surface-links via broken …
New theorem shows metrics of certain groups are close if their lengths are identical.
This is a survey on the project `Decorated Marked Surfaces', where we introduce the decoration on a marked surfaces , to study Calabi-Yau-2 (cluster) categories, Calabi-Yau-3 (Fukaya) categories, braid groups for quivers with potential, quadratic differentials and stability conditions.
Marked vertex diagrams provide a combinatorial way to represent knotted surfaces in ; including virtual crossings allows for a theory of virtual knotted surfaces and virtual cobordisms. Biquandle counting invariants are defined only for marked vertex diagrams representing knotted orientable surfaces; we e…
New invariant for surface-knots in 4D from marked graphs.
In earlier work the Kauffman bracket polynomial was extended to an invariant of marked graphs, i.e., looped graphs whose vertices have been partitioned into two classes (marked and not marked). The marked-graph bracket polynomial is readily modified to handle graphs with weighted vertices. We present formulas that simp…
The subject of this paper is the relationship among the marked length spectrum, the length spectrum, the Laplace spectrum on functions, and the Laplace spectrum on forms on Riemannian nilmanifolds. In particular, we show that for a large class of three-step nilmanifolds, if a pair of nilmanifolds in this class has the …
The subject of this paper is the relationship among the marked length spectrum, the length spectrum, the Laplace spectrum on functions, and the Laplace spectrum on forms on Riemannian nilmanifolds. In particular, we show that for a large class of three-step nilmanifolds, if a pair of nilmanifolds in this class has the …
Proposes a method to generate multivariate prediction intervals for random forests.
Study proves rigidity of marked length spectra in contracting group actions.
In earlier work we introduced the graph bracket polynomial of graphs with marked vertices, motivated by the fact that the Kauffman bracket of a link diagram D is determined by a looped, marked version of the interlacement graph associated to a directed Euler system of the universe graph of D. Here we extend the graph b…
Two Anosov metrics with same boundary distance are isometric.
Disk and sphere graphs embed quasi-isometrically in R^2.
The paper defines new representations and groups related to virtual links.