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.
Optimizes dividend policies in a Brownian model with controlled rates.
Study refracted skew Brownian motion, find densities and asymptotics.
In this paper, we introduce an insurance ruin model with adaptive premium rate, thereafter refered to as restructuring/refraction, in which classical ruin and bankruptcy are distinguished. In this model, the premium rate is increased as soon as the wealth process falls into the red zone and is brought back to its regul…
Machine learning models solve inverse eigenvalue problems for symmetric potentials and refractive indices.
This paper studies a class of optimal multiple stopping problems driven by Lévy processes. Our model allows for a negative effective discount rate, which arises in a number of financial applications, including stock loans and real options, where the strike price can potentially grow at a higher rate than the original d…
In this paper, we obtain analytical expression for the distribution of the occupation time in the red (below level ) up to an (independent) exponential horizon for spectrally negative Lévy risk processes and refracted spectrally negative Lévy risk processes. This result improves the existing literature in which only…
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…
In this paper we study perpetual American call and put options in an exponential Lévy model. We consider a negative effective discount rate which arises in a number of financial applications including stock loans and real options, where the strike price can potentially grow at a higher rate than the original discount f…
In this paper, we investigate Parisian ruin for a Lévy surplus process with an adaptive premium rate, namely a refracted Lévy process. More general Parisian boundary-crossing problems with a deterministic implementation delay are also considered. Our main contribution is a generalization of the result in Loeffen et al.…
In this paper we study a spectrally negative Lévy process which is refracted at its running maximum and at the same time reflected from below at a certain level. Such a process can for instance be used to model an insurance surplus process subject to tax payments according to a loss-carry-forward scheme together with t…
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 …
New system studies trapped light paths in Euclidean space.
Constructs flows on quotients of Lie groups for Anosov subgroups.
In the standard models for optimal multiple stopping problems it is assumed that between two exercises there is always a time period of deterministic length , the so called refraction period. This prevents the optimal exercise times from bunching up together on top of the optimal stopping time for the one-exercise c…
In this paper we study the Omega risk model with surplus-dependent tax payments in a time-homogeneous diffusion setting. The new model incorporates practical features from both the Omega risk model(Albrecher and Gerber and Shiu (2011)) and the risk model with tax(Albrecher and Hipp (2007)). We explicitly characterize t…
Characterizes flag geometries for Hitchin representations in SL3(R).
The point of the paper is to show some limitations of geometrical optics in the analysis of subwavelength focusing. We analyze the resolution of the image of a line source radiating in the Maxwell fisheye and the Veselago-Pendry slab lens. The former optical medium is deduced from the stereographic projection of a virt…
An integral stability estimate is proved for refraction coefficients of two conformal metrics in a plane domain in terms of its travel times. No assumption on absence of conjugate points of geodesics is made.
The works of William Rowan Hamilton in Geometrical Optics are presented, with emphasis on the Malus-Dupin theorem. According to that theorem, a family of light rays depending on two parameters can be focused to a single point by an optical instrument made of reflecting or refracting surfaces if and only if, before ente…
We study the multiplicity sets of first order symbols associated with differential operators on two dimensional surfaces. This work is inspired by the phenomenon of conical refraction explained by the existence of singularities in the Fresnel hyper-surface for Maxwell's equations on an anisotropic crystal.
We study an optimal multiple stopping problem for call-type payoff driven by a spectrally negative Levy process. The stopping times are separated by constant refraction times, and the discount rate can be positive or negative. The computation involves a distribution of the Levy process at a constant horizon and hence t…
In this paper, we study the dual representation for generalized multiple stopping problems, hence the pricing problem of general multiple exercise options. We derive a dual representation which allows for cashflows which are subject to volume constraints modeled by integer valued adapted processes and refraction period…
Generalizes Fermat's principle for wave propagation in cone structures.
This paper studies the optimal dividend problem with capital injection under the constraint that the cumulative dividend strategy is absolutely continuous. We consider an open problem of the general spectrally negative case and derive the optimal solution explicitly using the fluctuation identities of the refracted-ref…
Lie groupoids and their associated algebroids arise naturally in the study of the constitutive properties of continuous media. Thus, Continuum Mechanics and Differential Geometry illuminate each other in a mutual entanglement of theory and applications. Given any material property, such as the elastic energy or an inde…
It is shown that a lagrangian system whose Legendre transformation degenerates along a hypersurface behaves in a strange manner by jumping from time to time without any ''visible cause''. In such a jump the system changes instantaneously its coordinates as well as its momenta. The mathematical dscription of the phenome…
Consider the optimal dividend problem for an insurance company whose uncontrolled surplus precess evolves as a spectrally negative Levy process. We assume that dividends are paid to the shareholders according to admissible strategies whose dividend rate is bounded by a constant. The objective is to find a dividend poli…
In this paper we present the distinguished (d-) Riemannian geometry (in the sense of nonlinear connection, Cartan canonical linear connection, together with its d-torsions and d-curvatures) for a possible Lagrangian inspired by optics in non-uniform media. The corresponding equations of motion are also exposed, and som…
High frequency limit for most of wave phenomena is known as quasiclassical limit or ray optics limit. Propagation of waves in this limit is described in terms of wave fronts and rays. Wave front is a surface of constant phase whose points are moving along rays. As it appears, their motion can be described by Hamilton e…
Most distortion correction methods focus on simple forms of distortion, such as radial or linear distortions. These works undistort images either based on measurements in the presence of a calibration grid, or use multiple views to find point correspondences and predict distortion parameters. When possible distortions …
We survey some results on travel time tomography. The question is whether we can determine the anisotropic index of refraction of a medium by measuring the travel times of waves going through the medium. This can be recast as geometry problems, the boundary rigidity problem and the lens rigidity problem. The boundary r…
This paper revisits the problem of recovering a smooth, isotropic, layered wave speed profile from surface traveltime information. While it is classic knowledge that the diving (refracted) rays classically determine the wave speed in a weakly well-posed fashion via the Abel transform, we show in this paper that travelt…
Automates learning of multivariate diffusions for generative models.
Masking diffusion outperforms other discrete diffusion models by incorporating jump times into the model.
Diffusion-GAN uses diffusion to improve GAN training stability and realism.
Study shows how heat leaks from material sets in low diffusivity scenarios.
New blurring diffusion models bridge heat dissipation and denoising.
Study mass transport in low-diffusivity using Lagrangian coordinates.
New method tackles video inverse problems using image diffusion models.
Diffusion models generate new samples with active guidance, but theory is limited.
Unified framework for multi-view diffusion geometries using intertwined diffusion trajectories.
PaGoDA reduces diffusion model training costs by 64x.
Study shows diffused interface flows to single diffused balls over time.
Latent diffusion improves robustness in missing data imputation.
The paper examines smoothness in diffusion algebra.
DMPS uses diffusion maps and LAWGD for efficient generative modeling.
Develops a new model for pricing without arbitrage opportunities.
Investor-driven information diffusion affects excess comovement in China and the U.S. markets.