The Zariski-Lefschetz principle for higher homotopy groups of nongeneric pencils

We prove a general Zariski-van Kampen-Lefschetz type theorem for higher homotopy groups of generic and nongeneric pencils on singular open complex spaces.

Intermediate asymptotics beyond homogeneity and self-similarity: long time behavior for [formula]

"Vegeu el resum a l'inici del document del fitxer adjunt."

On the goodness of fit of Kirk's formula for spread option prices

In this paper we investigate the goodness of fit of the Kirk's approximation formula for spread option prices in the correlated lognormal framework. Towards this end, we use the Malliavin calculus techniques to find an expression for the short-time implied volatility skew of options with random strikes. In particular, we obtain that this skew is very pronounced in the case of spread options with extremely high correlations, which cannot be reproduced by a constant volatility approximation as in the Kirk's formula. This fact agrees with the empirical evidence. Numerical examples are given.

A general decomposition formula for derivative prices in stochastic volatility models

We see that the price of an european call option in a stochastic volatilityframework can be decomposed in the sum of four terms, which identifythe main features of the market that affect to option prices: the expectedfuture volatility, the correlation between the volatility and the noisedriving the stock prices, the market price of volatility risk and thedifference of the expected future volatility at different times. We alsostudy some applications of this decomposition.

A generalization of Hull and White formula and applications to option pricing approximation

By means of Malliavin Calculus we see that the classical Hull and White formulafor option pricing can be extended to the case where the noise driving thevolatility process is correlated with the noise driving the stock prices. Thisextension will allow us to construct option pricing approximation formulas.Numerical examples are presented.

A decomposition formula for option prices in the Heston model and applications to option pricing approximation

By means of classical Itô's calculus we decompose option prices asthe sum of the classical Black-Scholes formula with volatility parameterequal to the root-mean-square future average volatility plus a term dueby correlation and a term due to the volatility of the volatility. Thisdecomposition allows us to develop first and second-order approximationformulas for option prices and implied volatilities in the Heston volatilityframework, as well as to study their accuracy. Numerical examples aregiven.

A Hull and White formula for a general stochastic volatility jump-diffusion model with applications to the study of the short-time behavior of the implied volatility

In this paper, generalizing results in Alòs, León and Vives (2007b), we see that the dependence of jumps in the volatility under a jump-diffusion stochastic volatility model, has no effect on the short-time behaviour of the at-the-money implied volatility skew, although the corresponding Hull and White formula depends on the jumps. Towards this end, we use Malliavin calculus techniques for Lévy processes based on Løkka (2004), Petrou (2006), and Solé, Utzet and Vives (2007).

Evaluating solutions to process, view and listen mathematical formula within an accessible context

Proves de conversió de fòrmules matemàtiques des d'editors de text ofimàtics i des de Làtex. Visionat en HTML i MathML. El millor resultat s'aconsegueix amb MSWord+MathType i IE+MathPlayer.

Periodic points of holomorphic maps via Lefschetz numbers

In this paper we study the set of periods of holomorphic maps on compact manifolds, using the periodic Lefschetz numbers introduced by Dold and Llibre, which can be computed from the homology class of the map. We show that these numbers contain information about the existence of periodic points of a given period; and, if we assume the map to be transversal, then they give us the exact number of such periodic orbits. We apply this result to the complex projective space of dimension n and to some special type of Hopf surfaces, partially characterizing their set of periods. In the first case we also show that any holomorphic map of CP(n) of degree greater than one has infinitely many distinct periodic orbits, hence generalizing a theorem of Fornaess and Sibony. We then characterize the set of periods of a holomorphic map on the Riemann sphere, hence giving an alternative proof of Baker's theorem.

On Ito's formula for elliptic diffusion processes

Bardina and Jolis [Stochastic process. Appl. 69 (1997) 83-109] prove an extension of Ito's formula for F(Xt, t), where F(x, t) has a locally square-integrable derivative in x that satisfies a mild continuity condition in t and X is a one-dimensional diffusion process such that the law of Xt has a density satisfying certain properties. This formula was expressed using quadratic covariation. Following the ideas of Eisenbaum [Potential Anal. 13 (2000) 303-328] concerning Brownian motion, we show that one can re-express this formula using integration over space and time with respect to local times in place of quadratic covariation. We also show that when the function F has a locally integrable derivative in t, we can avoid the mild continuity condition in t for the derivative of F in x.

Chaotic Kabanov formula for the Azéma martingales

We derive the chaotic expansion of the product of nth- and first-order multiple stochastic integrals with respect to certain normal martingales. This is done by application of the classical and quantum product formulae for multiple stochastic integrals. Our approach extends existing results on chaotic calculus for normal martingales and exhibits properties, relative to multiple stochastic integrals, polynomials and Wick products, that characterize the Wiener and Poisson processes.

On an asymptotic formula for the maximum voltage drop in a on-chip power distribution network

We present a new asymptotic formula for the maximum static voltage in a simplified model for on-chip power distribution networks of array bonded integrated circuits. In this model the voltage is the solution of a Poisson equation in an infinite planar domain whose boundary is an array of circular pads of radius ", and we deal with the singular limit Ɛ → 0 case. In comparison with approximations that appear in the electronic engineering literature, our formula is more complete since we have obtained terms up to order Ɛ15. A procedure will be presented to compute all the successive terms, which can be interpreted as using multipole solutions of equations involving spatial derivatives of functions. To deduce the formula we use the method of matched asymptotic expansions. Our results are completely analytical and we make an extensive use of special functions and of the Gauss constant G

DOMINIQUE VALÉRIAN (ed.) (Cyrille Aillet, Sophie Gilotte, AnnelieseNef, Christophe Picard, Jean-Pierre Van Staëvel, Élise Voguet):Islamisation et arabisation de l’Occident musulman médiéval (VIIe–XIIesiècle)

This book is the result of a one-year seminar series"Islam médiéval d"Occident (VIIe-XVe)", held at the Colegio de España in Paris in 2006-07 by the Association des doctorants en histoire des mondes musulmans médievaux (Diwan http://diwan.hypotheses.org), and a second volume focusing on Arabization is expected (p. 33). The contributors" experience, alongside their university and research backgrounds, have led to the publication of articles of an outstandingly high level throughout this book. This scholarly achievement is combined with a thought-provoking theoretical framework, where Arabization and Islamization give a common theme to the proceedings, which are developed in four parts.