A triple comparison between anticipating stochastic integrals in financial modeling

We consider a simplified version of the problem of insider trading in a financial market. We approach it by means of anticipating stochastic calculus and compare the use of the Hitsuda-Skorokhod, the Ayed-Kuo, and the Russo-Vallois forward integrals within this context. Our results give some indication that, while the forward integral yields results with a suitable financial meaning, the Hitsuda-Skorokhod and the Ayed-Kuo integrals do not provide an appropriate formulation of this problem. Further results regarding the use of the Ayed-Kuo integral in this context are also provided, including the proof of the fact that the expectation of a Russo-Vallois solution is strictly greater than that of an Ayed-Kuo solution. Finally, we conjecture the explicit solution of an Ayed-Kuo stochastic differential equation that possesses discontinuous sample paths with finite probability

Dynamic Scaling of Non-Euclidean Interfaces

The dynamic scaling of curved interfaces presents features that are strikingly different from those of the planar ones. Spherical surfaces above one dimension are flat because the noise is irrelevant in such cases. Kinetic roughening is thus a one-dimensional phenomenon characterized by a marginal logarithmic amplitude of the fluctuations. Models characterized by a planar dynamical exponent $z>1$, which include the most common stochastic growth equations, suffer a loss of correlation along the interface, and their dynamics reduce to that of the radial random deposition model in the long time limit. The consequences in several applications are discussed, and we conclude that it is necessary to reexamine some experimental results in which standard scaling analysis was applied

Lepton masses and mixings in orbifold models with three Higgs families

We analyse the phenomenological viability of heterotic Z(3) orbifolds with two Wilson lines, which naturally predict three supersymmetric families of matter and Higgs fields. Given that these models can accommodate realistic scenarios for the quark sector avoiding potentially dangerous flavour-changing neutral currents, we now address the leptonic sector, finding that viable orbifold configurations can in principle be obtained. In particular,it is possible to accomodate present data on charged lepton masses, while avoiding conflict with lepton flavour-violating decays. Concerning the generation of neutrino masses and mixings, we find that Z(3) orbifolds offer several interesting possibilities.Comment: 28 pages, 11 figures. References adde

Stochastic growth equations on growing domains

The dynamics of linear stochastic growth equations on growing substrates is studied. The substrate is assumed to grow in time following the power law $t^\gamma$, where the growth index $\gamma$ is an arbitrary positive number. Two different regimes are clearly identified: for small $\gamma$ the interface becomes correlated, and the dynamics is dominated by diffusion; for large $\gamma$ the interface stays uncorrelated, and the dynamics is dominated by dilution. In this second regime, for short time intervals and spatial scales the critical exponents corresponding to the non-growing substrate situation are recovered. For long time differences or large spatial scales the situation is different. Large spatial scales show the uncorrelated character of the growing interface. Long time intervals are studied by means of the auto-correlation and persistence exponents. It becomes apparent that dilution is the mechanism by which correlations are propagated in this second case.Comment: Published versio

On the Geometric Principles of Surface Growth

We introduce a new equation describing epitaxial growth processes. This equation is derived from a simple variational geometric principle and it has a straightforward interpretation in terms of continuum and microscopic physics. It is also able to reproduce the critical behavior already observed, mound formation and mass conservation, but however does not fit a divergence form as the most commonly spread models of conserved surface growth. This formulation allows us to connect the results of the dynamic renormalization group analysis with intuitive geometric principles, whose generic character may well allow them to describe surface growth and other phenomena in different areas of physics

Leyes de conservación en el mundo físico : un estudio de caso desde la teoría de los campos conceptuales

Este análisis tiene como propósito emprender la reflexión acerca de la vasta cantidad de variables que se deberían tener en cuenta cuando se trabaja en temas a través de tareas y actividades cuya apariencia es de relativa baja significación y alta automatización, y sin embargo, pueden acarrear serias dificultades a los estudiantes. Es el caso de las leyes de conservación. Debemos reconocer que para lograr un desarrollo aceptable del mismo, es importante que el alumno se encuentre al menos en el umbral del uso de una organización esquemática básica. La teoría de los campos conceptuales de Vergnaud orienta el análisis y la formulación de algunas hipótesis preliminares