We investigate a new basic model for asset pricing, the hyperbolic model, which allows an almost perfect statistical t of stock return data. After a brief introduction into the theory supported by an appendix we use also secondary market data to compare the hyperbolic model to the classical Black-Scholes model. We study implicit volatilities, the smile e ect and the pricing performance. Exploit...

This note describes estimation algorithms for generalized hyperbolic hyperbolic and nor mal inverse Gaussian distributions These distributions provide a better t to empirically observed log return distributions of nancial assets than the classical normal distributions Based on the better t to the semi heavy tails of nancial assets we can compute more realistic Value at Risk estimates The modell...

A real polynomial P of degree n in one real variable is hyperbolic if its roots are all real. A real-valued function P is called a hyperbolic polynomial-like function (HPLF) of degree n if it has n real zeros and P (n) vanishes nowhere. Denote by x (i) k the roots of P , k = 1, . . . , n− i, i = 0, . . . , n− 1. Then in the absence of any equality of the form x (j) i = x (l) k (1) one has ∀i < ...

The primary objective of a gravity survey over a sedimentary basin is to delineate the shape of the basin. To fulfill this objective, information is needed about the densities within the sedimentary section. Densities of sedimentary rocks increase with depth (mainly due to compaction), approaching that of the basement in deep basins. Sedimentary basins are generally associated with low gravity ...

We obtain a system for the spatial metric and extrinsic curvature of a spacelike slice that is hyperbolic non-strict in the sense of Leray and Ohya and is equivalent to the Einstein equations. Its characteristics are the light cone and the normal to the slice for any choice of lapse and shift functions, and it admits a well-posed causal Cauchy problem in a Gevrey class of index α = 2. The syste...

Given a non-positively curved 2-complex with a circle-valued Morse function satisfying some extra combinatorial conditions, we describe how to locally isometrically embed this in a larger non-positively curved 2-complex with free-by-cyclic fundamental group. This embedding procedure is used to produce examples of CAT(0) free-by-cyclic groups that contain closed hyperbolic surface subgroups with...

We call Poincaré time the time associated to the Poincaré (or first return) map of a vector field. In this paper we prove the non-accumulation of isolated critical points of the Poincaré time T on hyperbolic polycycles of polynomial vector fields. The result is obtained by proving that the Poincaré time of a hyperbolic polycycle either has an unbounded principal part or is an almost regular fun...

Resonance asymptotics for asymptotically hyperbolic manifolds with warped-product ends By Pascal Philipp We study the spectral theory of asymptotically hyperbolic manifolds with ends of warped-product type. Our main result is an upper bound on the resonance counting function, with a geometric constant expressed in terms of the respective Weyl constants for the core of the manifold and the base ...

The Dirichlet problem and other nonclassical boundary value problems for linear hyperbolic equations with two independent variables have been the subject of various studies (see, e.g., [1]–[8], [10]–[16] and the references therein). However such problems for higher order nonlinear hyperbolic equations still remain unstudied. The present paper is an attempt to fulfill the existing gap. Let m and...