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 …

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…

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…

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…

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 $Vy=λy+f$.

The paper defines and analyzes Poissonian occupation times for negative Lévy processes.

The study finds sparse sets that uniquely determine metrics on negatively curved manifolds.

New proof shows certain 3D spaces are essentially like infinite space.

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…

The study proves Strichartz and spectral projection theorems on specific types of curved surfaces.

Sharp spectral estimates for negatively curved foliations.

The optimal dividend problem by De Finetti (1957) has been recently generalized to the spectrally negative Lévy model where the implementation of optimal strategies draws upon the computation of scale functions and their derivatives. This paper proposes a phase-type fitting approximation of the optimal strategy. We con…

Proposes RNSE for clustering with adaptive similarity matrix learning.

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

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 …

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 …

Researchers find spectral gaps in quantum flag manifolds using twisted operators.

New bounds on Bartnik mass for surfaces with non-negative first eigenvalue.

Optimal estimates for spectral projection norms on compact manifolds.

In this paper we consider the optimal dividend problem for an insurance company whose risk process evolves as a spectrally negative Lévy process in the absence of dividend payments. The classical dividend problem for an insurance company consists in finding a dividend payment policy that maximizes the total expected di…

A new method using negative-shifted gradient descent improves overparameterized linear regression by avoiding structural limitations of negative ridge endpoints.

Paper calculates the distribution of time spent below zero in risk models.

Study connects spectral properties to frame flows on curved manifolds.

The paper compares spectral geometry in hyperbolic and spherical manifolds.

Optimal stopping strategy for a Lévy process near its supremum.

In this paper we analyze so-called Parisian ruin probability that happens when surplus process stays below zero longer than fixed amount of time $ζ>0$. We focus on general spectrally negative Lévy insurance risk process. For this class of processes we identify expression for ruin probability in terms of some other quan…

Researchers approximate spectral targets on manifolds with constant negative curvature.

This paper optimizes periodic dividend strategies for Lévy processes with transaction costs.

The optimal capital structure model with endogenous bankruptcy was first studied by Leland (1994) and Leland and Toft (1996), and was later extended to the spectrally negative Levy model by Hilberink and Rogers (2002) and Kyprianou and Surya (2007). This paper incorporates the scale effects by allowing the values of ba…

On curved spaces, viscous fluids reach equilibrium quickly.

Study improves understanding of Ricci curvature in manifolds.

Constructs non-isometric iso-length-spectral surfaces.

Geodesic balls with non-negative Ricci curvature have a sharp lower bound on their first Dirichlet eigenvalue.

New gauge preserves Einstein metrics' interactions, proving rigidity on negatively curved manifolds.

Researchers study spectral asymmetry using pseudodifferential projections on the massless Dirac operator.

The study proves inequalities on curved spaces without global curvature bounds.

We argue that the standard graph Laplacian is preferable for spectral partitioning of signed graphs compared to the signed Laplacian. Simple examples demonstrate that partitioning based on signs of components of the leading eigenvectors of the signed Laplacian may be meaningless, in contrast to partitioning based on th…

New rigidity theorem for sharp spectral gap in nonnegatively curved spaces.

In this paper we consider dividend problem for an insurance company whose risk evolves as a spectrally negative Lévy process (in the absence of dividend payments) when Parisian delay is applied. The objective function is given by the cumulative discounted dividends received until the moment of ruin when so-called barri…

We consider the optimal stopping of a class of spectrally negative jump diffusions. We state a set of conditions under which the value is shown to have a representation in terms of an ordinary nonlinear programming problem. We establish a connection between the considered problem and a stopping problem of an associated…

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…

A novel method relaxes binary constraints to non-negative spheres for multi-matching and clustering.

We prove spectral, stochastic and mean curvature estimates for complete $m$-submanifolds $\varphi \colon M \to N$ of $n$-manifolds with a pole $N$ in terms of the comparison isoperimetric ratio $I_{m}$ and the extrinsic radius $r_\varphi\leq \infty$. Our proof holds for the bounded case $r_\varphi< \infty$, recovering …

New Bethe-Hessian method improves community detection in sparse networks.

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…

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 …

Regularized spectral methods improve clustering in signed graphs, especially for sparse data.

Length spectral rigidity is the question of under what circumstances the geometry of a surface can be determined, up to isotopy, by knowing only the lengths of its closed geodesics. It is known that this can be done for negatively curved Riemannian surfaces, as well as for negatively-curved cone surfaces. Steps are tak…