Related papers: Existence of L\'evy term structure models
This article presents a systematic methodology for modeling a class of flexible multidimensional mechanical structures defined by linear elastic relations that directly allows to obtain their infinite-dimensional port-Hamiltonian…
This paper is devoted to the study of degenerate critical elliptic equations of Caffarelli-Kohn-Nirenberg type. By means of blow-up analysis techniques, we prove an a-priori estimate in a weighted space of continuous functions. From this…
We consider the solutions of the Cauchy problem for a dyadic model of Euler equations. We prove global existence and uniqueness of Leray-Hopf solutions in a rather large class K that implies in particular global existence and uniqueness in…
In Figueroa-L\'opez et al. (2013), a second order approximation for at-the-money (ATM) option prices is derived for a large class of exponential L\'evy models, with or without a Brownian component. The purpose of this article is twofold.…
We prove a universal approximation theorem that allows to approximate continuous functionals of c\`adl\`ag (rough) paths uniformly in time and on compact sets of paths via linear functionals of their time-extended signature. Our main…
In the jet bundle description of Field Theories (multisymplectic models, in particular), there are several choices for the multimomentum bundle where the covariant Hamiltonian formalism takes place. As a consequence, several proposals for…
After defining non-Gaussian L\'evy processes for two-sided time, stochastic differential equations with such L\'evy processes are considered. Solution paths for these stochastic differential equations have countable jump discontinuities in…
In the framework of Lie transform and the global method of averaging, the normal forms of a multidimensional slow-fast Hamiltonian system are studied in the case when the flow of the unperturbed (fast) system is periodic and the induced…
It is known that a single mapping defined on one term of a differential graded vector space extends to a strongly homotopy Lie algebra structure on the graded space when that mapping satisfies two conditions. This strongly homotopy Lie…
In this paper, we investigate the Leray problem for steady Navier-Stokes system under full slip boundary conditions in a two dimensional channel with straight outlets. The existence of solutions with arbitrary flux in a general channel with…
We study Lie-Hamilton systems on the plane, i.e. systems of first-order differential equations describing the integral curves of a $t$-dependent vector field taking values in a finite-dimensional real Lie algebra of planar Hamiltonian…
Consider a complex Hamiltonian system and an integral curve. In this paper, we give an effective and efficient procedure to put the variational equation of any order along the integral curve in reduced form provided that the previous one is…
The structures $\langle M,\subseteq^M\rangle$ arising as the inclusion relation of a countable model of sufficient set theory $\langle M,\in^M\rangle$, whether well-founded or not, are all isomorphic. These structures $\langle…
We develop a general method for derivative pricing. This approach has its roots in Shannon's Information Theory. The notion of $\lambda$-analyticity of L\'{e}vy models is introduced on the basis of which new representations of the pricing…
This survey aims to review two decades of progress on exponential functionals of (possibly killed) real-valued L\'evy processes. Since the publication of the seminal survey by Bertoin and Yor, substantial advances have been made in…
An age-old controversy in mathematics concerns the necessity and the possibility of constructive proofs. The controversy has been rekindled by recent advances which demonstrate the feasibility of a fully constructive mathematics. This…
Models of dependent type theories are contextual categories with some additional structure. We prove that if a theory $T$ has enough structure, then the category $T\text{-}\mathbf{Mod}$ of its models carries the structure of a model…
In this article we show how to analyze the covariation of bond prices nonparametrically and robustly, staying consistent with a general no-arbitrage setting. This is, in particular, motivated by the problem of identifying the number of…
This paper investigates the long-time dynamics of solutions for an abstract nonlinear stochastic hydrodynamic-type equation driven by multiplicative L\'{e}vy noise. The framework encompasses several key hydrodynamical models, including the…
We find approximate solutions of partial integro-differential equations, which arise in financial models when defaultable assets are described by general scalar L\'evy-type stochastic processes. We derive rigorous error bounds for the…