arXiv research

Characterizes Fatou closedness for robust asset pricing.

Paper explores closedness properties of convex sets in rearrangement invariant spaces.

The paper shows equivalence between order closedness and σ(L^Φ,L^Ψ)-closedness in Orlicz spaces.

The strong Fatou property is crucial for risk measures' dual representations.

Extends Fatou theorem to bounded harmonic maps.

Extends risk measure theory to general Orlicz spaces.

Proves theorem for Riemannian manifolds, extending previous work.

Little is known about the global topology of the Fatou set $U(f)$ for holomorphic endomorphisms $f: \mathbb{CP}^k \to \mathbb{CP}^k$, when $k >1$. Classical theory describes $U(f)$ as the complement in $\mathbb{CP}^k$ of the support of a dynamically-defined closed positive $(1,1)$ current. Given any closed positive $(…

The paper characterizes risk measures with the Fatou property in function spaces.

Generalizing Cusick's theorem on the closedness of the classical Lagrange spectrum for the approximation of real numbers by rational ones, we prove that various approximation spectra are closed, using penetration properties of the geodesic flow in cusp neighbourhoods in negatively curved manifolds and a result of Mauco…

New technique explains convergence in ML models with data modifications.

Study dynamics of automorphisms on cubic surfaces and their connection to Painlevé 6.

Study of algebraic dynamics on Markov cubics in tropical geometry.

In this paper we study a class of functions that appear naturally in some equidistribution problems and that we call $F$-harmonic. These are functions of the universal cover of a closed and negatively curved which possess an integral representation analogous to the Poisson representation of harmonic functions, where th…

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New method avoids IV limitations for flexible estimation.

Investigates stability properties of Haezendonck-Goovaerts premium principles in Orlicz spaces.

Solves logarithmic ∂-equation on Kähler manifolds with smooth divisors.

The paper explores properties of functions on Teichmüller space, proving theorems about limits and non-ergodicity.

New risk measures for incomplete markets without lattice structures.

The study extends classical results on harmonic functions to Riemannian manifolds with non-tangential boundary limits.

Estimates for spacelike hypersurfaces in de Sitter space.

Study geodesics on compact Lorentzian solvmanifolds, finding conditions for closedness.

In this paper we extend a recent result of Collin-Rosenberg ({\it a solution to the minimal surface equation in the Euclidean disc has radial limits almost everywhere}) to a large class of differential operators in Divergence form. Moreover, we construct an example (in the spirit of \cite{CR2}) of a minimal graph in $\…

An infinite family of generalized pseudo-Anosov homeomorphisms of the sphere S is constructed, and their invariant foliations and singular orbits are described explicitly by means of generalized train tracks. The complex strucure induced by the invariant foliations is described, and is shown to make S into a complex sp…

Optimizes riskmetrics with uncertainty, making complex problems simpler.

We identify a large class of Orlicz spaces $X$ for which the topology $σ(X,X_n^\sim)$ fails the C-property introduced in [7]. We also establish a variant of the C-property and use it to prove a $w^*$-representation theorem for proper convex increasing functionals on dual Banach lattices that satisfy a suitable version …

Study collective pricing and hedging with admissible risk exchanges forming a finitely generated convex cone.

Integrable flows on the Grassmannians Gr(N-1,N+1) are defined by the requirement of closedness of the differential N-1 forms $Ω_{N-1}$ of rank N-1 naturally associated with Gr(N-1,N+1). Gauge-invariant parts of these flows, given by the systems of the N-1 quasi-linear differential equations, describe coisotropic deform…

We study the superreplication of contingent claims under model uncertainty in discrete time. We show that optimal superreplicating strategies exist in a general measure-theoretic setting; moreover, we characterize the minimal superreplication price as the supremum over all continuous linear pricing functionals on a sui…

In this note we show that for any proper action of a Banach--Lie group $G$ on a Banach manifold $M$, the corresponding tangent maps $\g \to T_x(M)$ have closed range for each $x \in M$, i.e., the tangent spaces of the orbits are closed. As a consequence, for each free proper action on a Hilbert manifold, the quotient $…

We provide further techniques to study the Dolbeault and Bott-Chern cohomologies of deformations of solvmanifolds by means of finite-dimensional complexes. By these techniques, we can compute the Dolbeault and Bott-Chern cohomologies of some complex solvmanifolds, and we also get explicit examples, showing in particula…

Neural networks cannot approximate certain functions in Sobolev spaces, leading to unbounded parameter growth.

We introduce a general setting for multidimensional dispersionless integrable hierarchy in terms of differential $m$-form $Ω_m$ with the coefficients satisfying the Plücker relations, which is gauge-invariantly closed and its gauge-invariant coordinates (ratios of coefficients) are (locally) holomorphic with respect to…

Method learns graph from data clusters using FCA.

We study superhedging of contingent claims with physical delivery in a discrete-time market model with convex transaction costs. Our model extends Kabanov's currency market model by allowing for nonlinear illiquidity effects. We show that an appropriate generalization of Schachermayer's robust no arbitrage condition im…

The paper explores applications of Gauduchon metrics in complex geometry.

Investigates the effects of nondominated sets of probability measures in robust models of finance.

We show that the results of ArXiv:1305.6008 on the Fundamental Theorem of Asset Pricing and the super-hedging theorem can be extended to the case in which the options available for static hedging (\emph{hedging options}) are quoted with bid-ask spreads. In this set-up, we need to work with the notion of \emph{robust no…

We introduce a new kind of Riemannian manifold that includes weakly-, pseudo- and pseudo projective- Ricci symmetric manifolds. The manifold is defined through a generalization of the so called Z tensor; it is named "weakly Z symmetric" and denoted by (WZS)_n. If the Z tensor is singular we give conditions for the exis…

We review the relations between compact complex manifolds carrying various types of Hermitian metrics (Kähler, balanced or {\it strongly Gauduchon}) and those satisfying the $\partial\bar\partial$-lemma or the degeneration at $E_1$ of the Frölicher spectral sequence, as well as the behaviour of these properties under h…

A real projective orbifold is an $n$-dimensional orbifold modeled on $\mathbb{RP}^n$ with the group $PGL(n+1, \mathbb{R})$. We concentrate on an orbifold that contains a compact codimension $0$ submanifold whose complement is a union of neighborhoods of ends, diffeomorphic to closed $(n-1)$-dimensional orbifolds times …

Let $(M, \om)$ be a symplectic manifold, endowed with a compatible almost complex structure J and the associated metric g . For any p \in {1, 2, ... (dim M)/2} the form $\Om := \frac{\om^p}{p!}$ is a calibration. More generally, dropping the closedness assumption on $\om$, we get an almost hermitian manifold $(M, \om, …

New risk measure extensions preserve key properties.

We study unbounded 2-dimensional metric polytopes such as those arising as Kähler quotients of complete Kähler 4-manifolds with two commuting symmetries and zero scalar curvature. Under a mild closedness condition, we obtain a complete classification of metrics on such polytopes, and as a result classify all possible m…

Abstract: Studies differential systems on compact Lie groups, extending Greenfield and Wallach's methods.

It has been shown that for each Killing-Yano (KY)-form accepted by an $n$-dimensional (pseudo)Riemannian manifold of arbitrary signature, two basic gravitational currents can be defined. Conservation of the currents are explicitly proved by showing co-exactness of the one and co-closedness of the other. Some general ge…

We construct a new type of locally homeomorphic quasiregular mappings in the 3-sphere and discuss their relation to the M.A.Lavrentiev problem, the Zorich map with an essential singularity at infinity, the Fatou's problem and a quasiregular analogue of domains of holomorphy in complex analysis. The construction of such…