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.
The Heights Theorem is extended to all Riemann surfaces with a first kind fundamental group.
problem Establishing the Heights Theorem for all Riemann surfaces.
method Extending the theorem to all surfaces with a first kind fundamental group, using measured laminations and straightening horizontal trajectories.
result The horizontal map is injective for arbitrary Riemann surfaces with a conformal hyperbolic metric.
Using Vovk's outer measure, which corresponds to a minimal superhedging price, the existence of quadratic variation is shown for "typical price paths" in the space of càdlàg functions possessing a mild restriction on the jumps directed downwards. In particular, this result includes the existence of quadratic variation …
We describe the space of measured foliations induced on a compact Riemann surface by meromorphic quadratic differentials. We prove that any such foliation is realized by a unique such differential q if we prescribe, in addition, the principal parts of q at the poles. This generalizes a theorem of Hubbard and …
A meromorphic quadratic differential with poles of order two, on a compact Riemann surface, induces a measured foliation on the surface, with a spiralling structure at any pole that is determined by the complex residue of the differential at the pole. We introduce the space of such measured foliations, and prove that f…
A natural generalization of interval exchange maps are linear involutions, first introduced by Danthony and Nogueira. Recurrent train tracks with a single switch which we call non-classical interval exchanges, form a subclass of linear involutions without flips. They are analogs of classical interval exchanges, and are…
Thurston's boundary to the universal Teichmüller space T(D) is the space PMLbdd(D) of projective bounded measured laminations of D. A geodesic ray in T(D) is of Teichmüller type if it shrinks vertical foliation of an integrable holomorphic quadratic differential. In a prio…
For a non-uniform lattice in SL(2,R), we consider excursions in cusp neighborhoods of a random geodesic on the corresponding finite area hyperbolic surface or orbifold. We prove a strong law for a certain partial sum involving these excursions. This generalizes a theorem of Diamond and Vaaler for continued fractions. I…
We discuss the class of "Quadratic Normal Volatility" models, which have drawn much attention in the financial industry due to their analytic tractability and flexibility. We characterize these models as the ones that can be obtained from stopped Brownian motion by a simple transformation and a change of measure that o…
We consider random walks on the mapping class group that have finite first moment with respect to the word metric, whose support generates a non-elementary subgroup and contains a pseudo-Anosov map whose invariant Teichmuller geodesic is in the principal stratum of quadratic differentials. We show that a Teichmuller ge…
Motivated by electricity consumption metering, we extend existing nonnegative matrix factorization (NMF) algorithms to use linear measurements as observations, instead of matrix entries. The objective is to estimate multiple time series at a fine temporal scale from temporal aggregates measured on each individual serie…
We consider a square-integrable semimartingale and investigate the convex order relations between its discrete, continuous and predictable quadratic variation. As the main results, we show that if the semimartingale has conditionally independent increments and symmetric jump measure, then its discrete realized variance…
Study proves existence of equilibrium in incomplete economies with discontinuous volatility.
problem Existence of incomplete Radner equilibrium with nondegenerate endogenous volatility.
method Established existence of solution for Markovian quadratic BSDEs with discontinuous generators using unique continuation and backward uniqueness.
result Existence of incomplete Radner equilibrium with nondegenerate endogenous volatility.
In this paper, we consider a supervised learning setting where side knowledge is provided about the labels of unlabeled examples. The side knowledge has the effect of reducing the hypothesis space, leading to tighter generalization bounds, and thus possibly better generalization. We consider several types of side knowl…
The paper studies how hyperbolic surfaces degenerate along harmonic map rays.
problem The degeneration of hyperbolic surfaces along harmonic map rays.
method Using Teichmüller space and holomorphic quadratic differentials, the authors show convergence of rescaled distance functions to the intersection number with a vertical measured foliation.
result Hyperbolic surfaces along the ray converge to the dual R-tree of the vertical measured foliation in the sense of Gromov-Hausdorff.
We apply a quadratic hedging scheme developed by Foellmer, Schweizer, and Sondermann to European contingent products whose underlying asset is modeled using a GARCH process and show that local risk-minimizing strategies with respect to the physical measure do exist, even though an associated minimal martingale measure …
Let Q be a connected component of a stratum in the space of quadratic differentials for a non-exceptional Riemann surface of finite type. We show that the probability measure on Q in the Lebesgue measure class which is invariant under the Teichmueller flow is obtained by Bowen's construction.
A new stochastic volatility model with quadratic drift prevents moment explosions and preserves stock price martingale property.
problem Avoiding moment explosions and preserving stock price martingale property in stochastic volatility models.
method Introduces a one-factor stochastic volatility model with quadratic drift and a linear dispersion function, showing that the quadratic term is crucial.
result The model prevents moment explosions and preserves the martingale property of the stock price process.
This paper concerns integral varifolds of arbitrary dimension in an open subset of Euclidean space with its first variation given by either a Radon measure or a function in some Lebesgue space. Pointwise decay results for the quadratic tilt-excess are established for those varifolds. The results are optimal in terms of…
We construct an example of a uniquely ergodic measured foliation on a surface such that the associated translation flow on the orientation double cover is minimal but not uniquely ergodic. We then prove a geometric criterion for the horizontal foliation of a quadratic differential to be uniquely ergodic. The second the…
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…
The runtime for Kernel Partial Least Squares (KPLS) to compute the fit is quadratic in the number of examples. However, the necessity of obtaining sensitivity measures as degrees of freedom for model selection or confidence intervals for more detailed analysis requires cubic runtime, and thus constitutes a computationa…
Statistical inference and information processing of high-dimensional data often require efficient and accurate estimation of their second-order statistics. With rapidly changing data, limited processing power and storage at the acquisition devices, it is desirable to extract the covariance structure from a single pass …