arXiv research

Study on risk contributions of portfolios using lambda quantile risk measures.

Despite the fact that the Euler allocation principle has been adopted by many financial institutions for their internal capital allocation process, a comprehensive description of Euler allocation seems still to be missing. We try to fill this gap by presenting the theoretical background as well as practical aspects. In…

Paper improves VaR risk allocation by avoiding zero probability events.

A 4-manifold is parallelizable if its Stiefel-Whitney and Pontryagin classes vanish.

A generalization of the Euler-Plateau problem to account for the energy contribution due to twisting of the bounding loop is proposed. Euler-Lagrange equations are derived in a parameterized setting and a bifurcation analysis is performed. A pair of dimensionless parameters govern bifurcations from a flat, circular gro…

New methods solve complex financial equations.

This research improves forecasting and testing of risk contributions using Expected Shortfall.

A tropical curve in $\mathbb R^{3}$ contributes to Gromov-Witten invariants in all genus. Nevertheless, we present a simple formula for how a given tropical curve contributes to Gromov-Witten invariants when we encode these invariants in a generating function with exponents of $λ$ recording Euler characteristic. Our ma…

In this paper, we consider the problem of existence and multiplicity of conformal metrics on a riemannian compact $4-$dimensional manifold $(M^4,g_0)$ with positive scalar curvature. We prove new exitence criterium which provides existence results for a dense subset of positive functions and generalizes Bahri-Coron and…

Develops a new method for risk diversification using dynamic risk measures.

In 1985, physicists Dixon, Harvey, Vafa and Witten studied string theories on Calabi-Yau orbifolds (cf. [DHVW]). An interesting discovery in their paper was the prediction that a certain physicist's Euler number of the orbifold must be equal to the Euler number of any of its crepant resolutions. This was soon related t…

We present a new methodology of computing incremental contribution for performance ratios for portfolio like Sharpe, Treynor, Calmar or Sterling ratios. Using Euler's homogeneous function theorem, we are able to decompose these performance ratios as a linear combination of individual modified performance ratios. This a…

Let $D$ be an oriented classical or virtual link diagram with directed universe $\vec{U}$. Let $C$ denote a set of directed Euler circuits, one in each connected component of $U$. There is then an associated looped interlacement graph $L(D,C)$ whose construction involves very little geometric information about the way …

Paper proves existence and computation of Risk Budgeting portfolios.

NDDV estimates data point value from a single stochastic trajectory.

The paper analyzes high-dimensional sphere solutions to the Nirenberg problem with residual mass.

New approach to rotational Weingarten surfaces using geometric momentum.

On a polarised surface, solutions of the Vafa-Witten equations correspond to certain polystable Higgs pairs. When stability and semistability coincide, the moduli space admits a symmetric obstruction theory and a $\mathbb C^*$ action with compact fixed locus. Applying virtual localisation we define invariants constant …

Let V be a compact real analytic surface with isolated singularities embedded in $R^N$, and assume its smooth part is equipped with a Riemannian metric that is induced from some analytic Riemannian metric on $R^N$. We prove: 1. Each point of V has a neighborhood which is quasi-isometric (naturally and 'almost isometric…

Generalizes beam models to include curvature and torsion.

New simulation approaches to evaluating path-dependent options without matrix inversion issues nor Euler bias are evaluated. They employ three main contributions: Stochastic approximation replaces regression in the LSM algorithm; Explicit weak solutions to stochastic differential equations are developed and applied to …

New Euler characteristics for groupoids generalize orbifold Euler characteristics.

The paper defines and calculates Euler characteristics for quandles.

Proves Euler characteristic of collapsing Alexandrov spaces.

Odd-dimensional orbifolds' Euler characteristic equals half of their boundary's.

The paper finds small exotic 4-manifolds with free abelian groups.

New evidence supports the Euler class one conjecture for tight contact structures.

Summarizes connections between Euler characteristic theorems and conjectures.

Expands Euler-Poincare characteristic to supergeometry.

It is well known that the Euler characteristic of an odd dimensional compact manifold is zero. An Euler complex is a combinatorial analogue of a compact manifold. We present here an elementary proof of the corresponding result for Euler complexes.

In this paper, we study Euler classes in groups of homeomorphisms of Seifert fibered 3-manifolds. We show that, in contrast to the familiar Euler class for $\mathrm{Homeo}_0(S^1)^δ$, these Euler classes for $\mathrm{Homeo}_0(M^3)^δ$ are unbounded classes. In fact, we give examples of flat topological M bundles over a g…

We prove Witten's formula relating the Donaldson and Seiberg-Witten series modulo powers of degree $c+2$, with $c=-{1/4}(7χ+11σ)$, for four-manifolds obeying some mild conditions, where $χ$ and $σ$ are their Euler characteristic and signature. We use the moduli space of SO(3) monopoles as a cobordism between a link of …

Extends Zeitlin's model to 3-D axisymmetric Euler equations.

Schwarzian derivative connects to Euler-Lagrange equations in variational calculus.

This work begins by establishing a mathematical formalization between different geometrical interpretations of Neural Networks, providing a first contribution. From this starting point, a new interpretation is explored, using the idea of implicit vector fields moving data as particles in a flow. A new architecture, Vec…

Co-Euler structures were studied by Burghelea and Haller on closed manifolds as dual objects to Euler structures. We extend the notion of co-Euler structures to the situation of compact manifolds with boundary. As an application, by studying their variation with respect to smooth changes of the Riemannian metric, co-Eu…

Shows Euler-like vector fields come from specific embeddings.

Euler calculus is based on integrating simple functions with respect to the Euler characteristic. This paper makes the case for extending Euler calculus to continuous integrands by integrating with respect to (Gaussian) curvature. This requires a metric but is nevertheless defined within any O-minimal theory. It satisf…

Euler derived elastica equation using modern mathematical concepts.

We introduce the $Γ$-Euler-Satake characteristics of a general orbifold $Q$ presented by an orbifold groupoid $\mathcal{G}$, generalizing to orbifolds that are not necessarily global quotients the generalized orbifold Euler characteristics of Bryan-Fulman and Tamanoi. Each of these Euler characteristics is defined as t…

The paper derives a local formula for the Euler number of circle bundles.

Study Euler obstruction of 1-forms on determinantal singularities.

We study the asymptotic behavior of the difference $Δρ^{X, Y}_α:= ρ_α(X + Y) - ρ_α(X)$ as $α\rightarrow 1$, where $ρ_α$ is a risk measure equipped with a confidence level parameter $0 < α< 1$, and where $X$ and $Y$ are non-negative random variables whose tail probability functions are regularly varying. The case where …

Delisle's projection explained by Euler in 18th century.

Euler explored spherical geometry using trigonometric formulae and solid geometry methods.

Extends Euler class result to symplectic group.

Proves an Euler-type formula for Möbius strip partitions.

Formula for Euler characteristic of moduli spaces of Abelian differentials.