Newton-Okounkov bodies on projective bundles over curves

In this article, we study Newton-Okounkov bodies on projective vector bundles over curves. Inspired by Wolfe's estimates used to compute the volume function on these varieties, we compute all Newton-Okounkov bodies with respect to linear flags. Moreover, we characterize semi-stable vector bundles over curves via Newton-Okounkov bodies.Comment: 28 pages. Final version: to appear in Mathematische Zeitschrif

On singular Fano varieties with a divisor of Picard number one

In this paper we study the geometry of mildly singular Fano varieties on which there is an effective prime divisor of Picard number one. Afterwards, we address the case of toric varieties. Finally, we treat the lifting of extremal contractions to universal covering spaces in codimension 1.Comment: 35 pages. Final version: to appear in Annali della Scuola Normale Superiore, Classe di Scienz

Partial Derivative Approach for Option Pricing in a Simple Stochastic Volatility Model

We study a market model in which the volatility of the stock may jump at a random time from a fixed value to another fixed value. This model was already described in the literature. We present a new approach to the problem, based on partial derivative equations, which gives a different perspective to the problem. Within our framework we can easily consider several prescriptions for the market price of volatility risk, and interpret their financial meaning. Thus, we recover solutions previously cited in the literature as well as obtain new ones.Comment: 21 pages, 3 figures, submitted for publicatio

Amphisbaena cegei

Number of Pages: 3Integrative BiologyGeological Science

Numerical analysis of fractional charge solutions on the torus

We study by numerical methods a particular kind of SU(N) Yang-Mills solutions of the Euclidean equations of motion which appear on the torus when twisted boundary conditions are imposed. These are instanton-like configurations with the peculiarity of having fractional topological charge. We focus on those solutions with minimal non-trivial action $S=8\pi^2/\N$ and extract their properties in a few different cases, paying special attention to the $N \to \infty$ limit.Comment: 30 pages, 15 figure

Perpetual American options within CTRW's

Continuous-time random walks are a well suited tool for the description of market behaviour at the smallest scale: the tick-to-tick evolution. We will apply this kind of market model to the valuation of perpetual American options: derivatives with no maturity that can be exercised at any time. Our approach leads to option prices that fulfil financial formulas when canonical assumptions on the dynamics governing the process are made, but it is still suitable for more exotic market conditions.Comment: elsart, 12 pages, 2 figures, presented at APFA 6 conference; Revised and condensed version: 8 page

Exploración de potenciales productos de turismo náutico entre Puerto Mont y el Golfo del Corcovado, X Región, Chile

Tesis (Administrador en Ecoturismo)RESUMEN: Esta memoria consiste en el estudio de la zona comprendida entre Puerto Montt y el Golfo del Corcovado para determinar potenciales que ofrece el área para el Turismo Náutico, además contempla una revisión de la industria náutica a nivel mundial y nacional. En base a la información recopilada se realiza una evaluación de una propuesta de modelo de negocios de turismo náutico para el área, en el que se utiliza el supuesto de la compra de un yate a vela de 35 pies que realiza rutas de navegación por los más importantes atractivos naturales y culturales de la región. A través de esta evaluación se comprobó que el turismo náutico en yates no es rentable dentro de los parámetros que se utilizaron en la evaluación. Pero también se concluye que los magníficos atributos que posee esta zona son inigualables lo que habre interesantes oportunidades para el turismo de intereses especiales y dentro de ellos el Turismo náutico y el Ecoturismo.ABSTRACT: This thesis consists in the study of the area between Puerto Montt and the Corcovado Gulf to determine the potentials that the area offers to nautical tourism, and it also contemplates a review ofthe nautical industry at a national and World leve!. Based on the information gathered, an evaluation is done of a business proposal model of the nautical tourism for this area, in which a sail yacht of 35 feet is supposedly bought, navigating the routes through the most important natural and cultural attractions of the region. Through this evaluation it was proven that the nautical tourism for yachts is not profitable in the parameters that were used in the evaluation. But it is also conc1uded that the magnificent attributes that this area has, are unrivalled, and which opens interesting opportunities for special interests tourism and in that the nautical tourism and ecoturism