arXiv research

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 …

This article is devoted to the maximisation of HARA utilities of L{é}vy switching process on finite time interval via dual method. We give the description of all f-divergence minimal martingale measures in initially enlarged filtration, the expression of their Radon-Nikodym densities involving Hellinger and Kulback-Lei…

This paper presents generalized momentum mappings for covariant Hamiltonian field theories. The new momentum mappings arise from a generalization of symplectic geometry to $L_VY$, the bundle of vertically adapted linear frames over the bundle of field configurations $Y$. Specifically, the generalized field momentum obs…

In this paper, we study the ruin problem with investment in a general framework where the business part X is a L{é}vy process and the return on investment R is a semimartingale. We obtain upper bounds on the finite and infinite time ruin probabilities that decrease as a power function when the initial capital increases…

In this paper we consider a modified version of the classical optimal dividends problem of de Finetti in which the dividend payments subject to a penalty at ruin. We assume that the risk process is modeled by a general spectrally positive Levy process before dividends are deducted. Using the fluctuation theory of spect…

The paper finds optimal threshold strategies for insurance companies with a positive terminal value at creeping ruin.

We introduce a class of interest rate models, called the $α$-CIR model, which gives a natural extension of the standard CIR model by adopting the $α$-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 …

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 consider a version of the stochastic inventory control problem for a spectrally positive Lévy demand process, in which the inventory can only be replenished at independent exponential times. We show the optimality of a periodic barrier replenishment policy that restocks any shortage below a certain threshold at each…

This paper considers magnitude, asymptotics and duration of drawdowns for some Lévy processes. First, we revisit some existing results on the magnitude of drawdowns for spectrally negative Lévy processes using an approximation approach. For any spectrally negative Lévy process whose scale functions are well-behaved at …

A new method for nonstationary Gaussian processes using Fourier features.

Let $M$ be a manifold, $V$ be a vector field on $M$, and $B$ be a Banach space. For any fixed function $f:M\rightarrow B$ and any fixed complex number $λ$, we study Hyers-Ulam stability of the global differential equation $Vy=λy+f$.

Study optimal periodic dividend strategies for risky businesses with transaction costs.

In this paper we study the optimal dividend problem for a company whose surplus process evolves as a spectrally positive Levy process. This model including the dual model of the classical risk model and the dual model with diffusion as special cases. We assume that dividends are paid to the shareholders according to ad…

Proposes a Gaussian process for graph signals using adaptive spectral kernels.

Constructs supermartingale couplings with full marginals constraints.

We consider the optimal prediction problem of stopping a spectrally negative Lévy process as close as possible to a given distance $b \geq 0$ from its ultimate supremum, under a squared error penalty function. Under some mild conditions, the solution is fully and explicitly characterised in terms of scale functions. We…

IDPGs extend RDPGs with a Poisson process for random latent positions.

New spectral mixture representation for isotropic kernels simplifies random Fourier features.

In this paper, we revisit the optimal periodic dividend problem, in which dividend payments can only be made at the jump times of an independent Poisson process. In the dual (spectrally positive Lévy) model, recent results have shown the optimality of a periodic barrier strategy, which pays dividends at Poissonian divi…

In this paper, we provide a representation theorem for dynamic capital allocation under It{ô}-L{é}vy model. We consider the representation of dynamic risk measures defined under Backward Stochastic Differential Equations (BSDE) with generators that grow quadratic-exponentially in the control variables. Dynamic capital …

Transformer models show distinct spectral fingerprints under voice changes.

Paper shows graphs can be embedded in lower dimensions than expected.

This paper studies game-type credit default swaps that allow the protection buyer and seller to raise or reduce their respective positions once prior to default. This leads to the study of an optimal stopping game subject to early default termination. Under a structural credit risk model based on spectrally negative Le…

In this paper we propose a family of tractable kernels that is dense in the family of bounded positive semi-definite functions (i.e. can approximate any bounded kernel with arbitrary precision). We start by discussing the case of stationary kernels, and propose a family of spectral kernels that extends existing approac…

Fast simulates Volterra processes using RFF, focusing on S-fBM.

Introduces spectral-domain Wasserstein distance and Gelbrich bound for elliptical processes.

Numerous methods for computing conformal mesh paramterizations has been developed due to the vast applications in the field of geometry processing. Spectral conformal parameterization (SCP) is one of these methods to computing a quality conformal parameterization based on the spectral technique. SCP focus on a generali…

In this note we find a formula for the supremum distribution of spectrally positive or negative Lévy processes with a broken linear drift. This gives formulas for ruin probabilities in the case when two insurance companies (or two branches of the same company) divide between them both claims and premia in some specifie…

Positive scalar curvature metrics on cobordisms yield only reducible Seiberg-Witten solutions.

Spectro-Riemannian Graph Neural Networks integrate spectral and curvature signals for better graph representation learning.

Study surfaces with nonnegative curvature in spectral sense, proving inequalities and bounds.

The paper proves conditions for Kähler and Riemannian manifolds to be simply connected.

For graphs generated from stochastic blockmodels, adjacency spectral embedding is asymptotically consistent. Further, adjacency spectral embedding composed with universally consistent classifiers is universally consistent to achieve the Bayes error. However when the graph contains private or sensitive information, trea…

Improved spectral projection estimates on manifolds of non-positive curvature.

Spectral sparsification improves Gaussian graphical models under MTP2 constraints.

Define mass invariant for asymptotically hyperbolic 3-manifolds with toroidal infinity.

This paper improves spectral clustering for large datasets using the Nystrom method.

New method efficiently learns positive-definite curvature for neural nets.

Graph spectral analysis can yield meaningful embeddings of graphs by providing insight into distributed features not directly accessible in nodal domain. Recent efforts in graph signal processing have proposed new decompositions-e.g., based on wavelets and Slepians-that can be applied to filter signals defined on the g…

We consider a stable Cox--Ingersoll--Ross process driven by a standard Wiener process and a spectrally positive strictly stable Lévy process, and we study asymptotic properties of the maximum likelihood estimator (MLE) for its growth rate based on continuous time observations. We distinguish three cases: subcritical, c…

Positive weights improve kernel quadrature's accuracy.

The paper bounds bandwidth and focal radius for manifolds with positive isotropic curvature.

A new method for spectral positional encodings in directed graphs using Hermitian block Krylov subspaces.

We revisit the dividend payment problem in the dual model of Avanzi et al. ([2], [1], and [3]). Using the fluctuation theory of spectrally positive Lévy processes, we give a short exposition in which we show the optimality of barrier strategies for all such Lévy processes. Moreover, we characterize the optimal barrier …

The paper validates Stokes' theorem for differential subcomplexes in positively graded Lie groups.

Study spectral flow for Callias operators to prove obstructions to positive scalar curvature.

In this note we give, for a spectrally negative Levy process, a compact formula for the Parisian ruin probability, which is defined by the probability that the process exhibits an excursion below zero, with a length that exceeds a certain fixed period r. The formula involves only the scale function of the spectrally ne…