Nonparametric estimation for Levy processes with a view towards mathematical finance

Nonparametric methods for the estimation of the Levy density of a Levy process are developed. Estimators that can be written in terms of the ``jumps'' of the process are introduced, and so are discrete-data based approximations. A model selection approach made up of two steps is investigated. The first step consists in the selection of a good estimator from a linear model of proposed Levy densities, while the second is a data-driven selection of a linear model among a given collection of linear models. By providing lower bounds for the minimax risk of estimation over Besov Levy densities, our estimators are shown to achieve the ``best'' rate of convergence. A numerical study for the case of histogram estimators and for variance Gamma processes, models of key importance in risky asset price modeling driven by Levy processes, is presented.Comment: 68 pages, 19 figures, submitted to Annals of Statistic

Dynamic Credit Investment in Partially Observed Markets

We consider the problem of maximizing expected utility for a power investor who can allocate his wealth in a stock, a defaultable security, and a money market account. The dynamics of these security prices are governed by geometric Brownian motions modulated by a hidden continuous time finite state Markov chain. We reduce the partially observed stochastic control problem to a complete observation risk sensitive control problem via the filtered regime switching probabilities. We separate the latter into pre-default and post-default dynamic optimization subproblems, and obtain two coupled Hamilton-Jacobi-Bellman (HJB) partial differential equations. We prove existence and uniqueness of a globally bounded classical solution to each HJB equation, and give the corresponding verification theorem. We provide a numerical analysis showing that the investor increases his holdings in stock as the filter probability of being in high growth regimes increases, and decreases his credit risk exposure when the filter probability of being in high default risk regimes gets larger

Dose distribution calculation for in-vivo X-ray fluorescence scanning

In-vivo X-ray fluorescence constitutes a useful and accurate technique, worldwide established for constituent elementary distribution assessment. Actually, concentration distributions of arbitrary user-selected elements can be achieved along sample surface with the aim of identifying and simultaneously quantifying every constituent element. The method is based on the use of a collimated X-ray beam reaching the sample. However, one common drawback for considering the application of this technique for routine clinical examinations was the lack of information about associated dose delivery. This work presents a complete study of the dose distribution resulting from an in-vivo X-ray fluorescence scanning for quantifying biohazard materials on human hands. Absorbed dose has been estimated by means of dosimetricmodels specifically developed to this aim. In addition, complete dose distributions have been obtained by means of full radiation transport calculations in based on stochastic Monte Carlo techniques. A dedicated subroutine has been developed using the PENELOPE 2008 main code also integrated with dedicated programs -MatLab supported- for 3D dose distribution visualization. The obtained results show very good agreement between approximate analytical models and full descriptions by means of Monte Carlo simulations.La Fluorescencia de rayos-X in-vivo constituye una técnica útil y precisa, establecida ampliamente para la evaluación de constituyente de distribución primaria. De hecho las distribuciones de concentración de un elemento seleccionado arbitrariamente por el usuario se pueden lograr a lo largo de la superficie de la muestra con el objetivo de identificar y cuantificar simultáneamente cada elemento constituyente. El método se basa en el uso de un haz colimado de rayos X que incide en la muestra. Sin embargo, un inconveniente común para considerar la aplicación de esta técnica para exámenes clínicos de rutina es la falta de información sobre la administración de la dosis correspondiente. Este trabajo presenta un estudio completo de la distribución de la dosis resultante de un barrido in-vivo de Fluorescencia de rayos X para la cuantificacio ́n de los materiales biológicos peligrosos en manos humanas. La dosis absorbida se ha estimado por medio de modelos dosimétricos específicamente desarrollados para este fin. Además, las distribuciones de dosis completas se han obtenido por medio de cálculos de transporte de radiación completo en base a técnicas estocásticas de Monte Carlo. Una subrutina dedicada ha sido desarrollada utilizando el código principal PENELOPE 2008 también integrada con programas dedicados de soporte MatLab para la visualización 3D de la distribución de dosis. Los resultados obtenidos muestran una buena concordancia entre los modelos analíıticos aproximados y en todas las descripciones por medio de simulaciones de Monte Carlo.Fil: Figueroa, Rodolfo. Universidad De La Frontera. Dep de Ciencias Físicas; Chile;Fil: Lozano, Enrique. Instituto Nacional del Cancer. Unidad de Física Médica; Chile;Fil: Valente, Mauro Andres. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico - Conicet - Cordoba. Instituto de Fisica Enrique Gaviola; Argentina

Depreciación del Capital Natural, Ingreso y Crecimiento Sostenible: Lecciones de la Experiencia Chilena

The optimal exploitation of the natural resource base is crucial to attain maximum social welfare, especially in developing countries whose economies are highly dependent on such resources. This paper presents a simple model to correct the Gross Domestic Product (GDP) to obtain a measure of economic income, by subtracting from the Net National Product (NNP) the depreciation of natural capital. Corrected measures of the economic income for the period 1985-1997 are presented, taking into consideration mining and fishing resources and air contamination. The results show that approximately 3% of Chile’s economic income correspond to depreciation of its natural resources plus the cost of atmospheric pollution. In addition, genuine measures of saving are calculated. The results lead to the conclusion that economic growth was sustainable during the period 1985-1997. Important policy implications are obtained for a better management of natural resources in the future.