Option valuation as an expectation in the complex domain: The Black-Scholes case

It is very well known that the first succesful valuation of a stock option was done by solving a deterministic partial differential equation (PDE) of the parabolic type with some complementary conditions specific for the option. In this approach, the randomness in the option value process is eliminated through a no-arbitrage argument. An alternative approach is to construct a replicating portfolio for the option. From this viewpoint the payoff function for the option is a random process which, under a new probabilistic measure, turns out to be of a special type, a martingale. Accordingly, the value of the replicating portfolio (equivalently, of the option) is calculated as an expectation, with respect to this new measure, of the discounted value of the payoff function. Since the expectation is, by definition, an integral, its calculation can be made simpler by resorting to powerful methods already available in the theory of analytic functions. In this paper we use precisely two of those techniques to find the well-known value of a European call

Power variation of some integral fractional processes

We consider the asymptotic behaviour of the realized power variation of processes of the form ¿t0usdBHs, where BH is a fractional Brownian motion with Hurst parameter H E(0,1), and u is a process with finite q-variation, q<1/(1¿H). We establish the stable convergence of the corresponding fluctuations. These results provide new statistical tools to study and detect the long-memory effect and the Hurst parameter.

Stochastic differential equations with random coefficients

In this paper we establish the existence and uniqueness of a solution for different types of stochastic differential equation with random initial conditions and random coefficients. The stochastic integral is interpreted as a generalized Stratonovich integral, and the techniques used to derive these results are mainly based on the path properties of the Brownian motion, and the definition of the Stratonovich integral.

Approximation and support theorem for a wave equation in two space dimensions

We prove a characterization of the support of the law of the solution for a stochastic wave equation with two-dimensional space variable, driven by a noise white in time and correlated in space. The result is a consequence of an approximation theorem, in the convergence of probability, for equations obtained by smoothing the random noise. For some particular classes of coefficients, approximation in the Lp-norm for p¿1 is also proved.

Stochastic delay differential equations driven by fractional Brownian motion with Hurst parameter H 1/2

We consider the Cauchy problem for a stochastic delay differential equation driven by a fractional Brownian motion with Hurst parameter H>¿. We prove an existence and uniqueness result for this problem, when the coefficients are sufficiently regular. Furthermore, if the diffusion coefficient is bounded away from zero and the coefficients are smooth functions with bounded derivatives of all orders, we prove that the law of the solution admits a smooth density with respect to Lebesgue measure on R.

Coisotropic regularization of singular Lagrangians

We present an alternative approach to the usual treatments of singular Lagrangians. It is based on a Hamiltonian regularization scheme inspired on the coisotropic embedding of presymplectic systems. A Lagrangian regularization of a singular Lagrangian is a regular Lagrangian defined on an extended velocity phase space that reproduces the original theory when restricted to the initial configuration space. A Lagrangian regularization does not always exists, but a family of singular Lagrangians is studied for which such a regularization can be described explicitly. These regularizations turn out to be essentially unique and provide an alternative setting to quantize the corresponding physical systems. These ideas can be applied both in classical mechanics and field theories. Several examples are discussed in detail. 1995 American Institute of Physics.

Un programa psicosocial: programa psicoestimulatiu integral (P.P.I.) amb persones afectades de malaltia d' Alzheimer

L'any 2011 la malaltia d'Alzheimer es situava com la quarta causa de mort més freqüent amb un augment de fins a 11.907, més del doble de morts que l'any 2000 (INE). Aquestes dades demostren l'augment del número de persones que pateixen una demència a mesura que envelleixen i una de les explicacions és l'augment de l'esperança de vida. Per aquest motiu l'estudi de la qualitat de vida ha adquirit una gran importància des de la dècada dels 90. La qualitat de vida és un concepte especialment subjectiu pel fet que cada persona la viu segons la pròpia percepció de salut i benestar i el grau d'adaptació a l'entorn que l'envolta. Per aquest motiu es planteja un programa de psicoestimulació integral (PPI) centrat en les individualitats de cada persona: valors, interessos, història ocupacional..., des de la filosofia de la Teràpia Ocupacional. El projecte està elaborat mitjançant la metodologia qualitativa utilitzant l'enquesta en profunditat semi-estructurada per a realitzar les entrevistes i obtenir la informació principal a l'inici i al final del programa juntament amb tota la informació que s'obtingui de l'observació participant del dia a dia de cada un dels professionals per tal d'estudiar fins a quin punt aquesta atenció centrada en la persona contribueix a millorar la qualitat de vida de les persones afectades de Malaltia d'Alzheimer que reben tractaments no farmacològics com el proposat en aquest projecte. Com a tot estudi es poden trobar alguns factors condicionants com pot ser l'evolució pròpia de la malaltia amb les conseqüències negatives que això comporta i/o el número de participants que formen la mostra.

Generation of symmetric periodic orbits by a heteroclinic loop formed by two singular points and their invariant manifolds of dimension 1 and 2 in R3

In this paper we will find a continuous of periodic orbits passing near infinity for a class of polynomial vector fields in R3. We consider polynomial vector fields that are invariant under a symmetry with respect to a plane and that possess a “generalized heteroclinic loop” formed by two singular points e+ and e− at infinity and their invariant manifolds � and . � is an invariant manifold of dimension 1 formed by an orbit going from e− to e+, � is contained in R3 and is transversal to . is an invariant manifold of dimension 2 at infinity. In fact, is the 2–dimensional sphere at infinity in the Poincar´e compactification minus the singular points e+ and e−. The main tool for proving the existence of such periodic orbits is the construction of a Poincar´e map along the generalized heteroclinic loop together with the symmetry with respect to .

Symmetric periodic orbits near a heteroclinic loop in R3 formed by two singular points, a semistable periodic orbit and their invariant manifolds

In this paper we consider C1 vector fields X in R3 having a “generalized heteroclinic loop” L which is topologically homeomorphic to the union of a 2–dimensional sphere S2 and a diameter connecting the north with the south pole. The north pole is an attractor on S2 and a repeller on . The equator of the sphere is a periodic orbit unstable in the north hemisphere and stable in the south one. The full space is topologically homeomorphic to the closed ball having as boundary the sphere S2. We also assume that the flow of X is invariant under a topological straight line symmetry on the equator plane of the ball. For each n ∈ N, by means of a convenient Poincar´e map, we prove the existence of infinitely many symmetric periodic orbits of X near L that gives n turns around L in a period. We also exhibit a class of polynomial vector fields of degree 4 in R3 satisfying this dynamics.

Symmetric periodic orbits near a heteroclinic loop formed by two singular points and their invariant manifolds of dimension 1 and 2

In this paper we consider vector fields in R3 that are invariant under a suitable symmetry and that posses a “generalized heteroclinic loop” L formed by two singular points (e+ and e −) and their invariant manifolds: one of dimension 2 (a sphere minus the points e+ and e −) and one of dimension 1 (the open diameter of the sphere having endpoints e+ and e −). In particular, we analyze the dynamics of the vector field near the heteroclinic loop L by means of a convenient Poincar´e map, and we prove the existence of infinitely many symmetric periodic orbits near L. We also study two families of vector fields satisfying this dynamics. The first one is a class of quadratic polynomial vector fields in R3, and the second one is the charged rhomboidal four body problem.

Implementació d'un sistema integral d'impressió a l'empresa LaRoba

L'objectiu del projecte és implementar una solució integral de gestió d'impressió que proporcioni a l'empresa LaRoba un perfecte control sobre els dispositius i un estalvi substancial en els costos globals derivats de la impressió de documents.

Libro de Actas II Congreso Español de Gestión Integral de Deyecciones Ganaderas

Postprint (published version)

Plan integral de enfermería para la atención domiciliaria de pacientes con enfermedad neuromuscular e insuficiencia respiratoria

Las enfermedades neuromuscualres son enfermedades neurológicas, de naturaleza progresiva, normalmente hereditarias cuya principal característica clínica es la debilidad muscular. Dentro de las enfermedades que causan problemas respiratorios, existen una gran variedad de enfermedades neuromusculares que comprometen la función respiratoria, las cuales pueden dividirse en enfermedades neuromusculares neuropaticas y miopáticas, además de poder clasificarlas según la evolución. Las ENM pueden comprometer el sistema respiratorio condicionando morbilidad respiratoria de intensidad y precocidad variable dependiendo del grado de afección de los músculos respiratorios y deglutorios, así como de otros factores como el estado nutricional o la capacidad de deambulación, todos ellos factores que pueden ser incluidos dentro de un programa de enfermería de atención a domicilio.