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Duration models and value at risk using high-frequency data for the peruvian stock marketTéllez De Vettori, Giannio, Najarro Chuchón, Ricardo 20 February 2017 (has links)
Most empirical studies in nance use data on a daily basis which is obtained by retaining
the last observation of the day and ignoring all intraday records. However, as a result of
the increased automatization of nancial markets and the evolution of computational trading
systems, intraday data bases that record every transaction along with their characteristics have
been stablished. These data sets prompted the development of a new area of research ( nance
with high frequency data), and in 1980 a literature based on the mechanisms of trading began
(forms of trading, rules on securities trading, market structure, etc.), originating the Theory
of Market Microstructure for the valuation of nancial assets, whose models advocate that
timing transmits information. Then the literature proposed an extension to risk management
by calculating the implied volatility, which is estimated by the realized volatility on an intraday
level, and its applications for a ner value at risk (VaR).
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Análisis de la monotonicidad de la demanda vía relaciones de preferencia y funciones de utilidadYarasca Moscol, Julio Eduardo 01 January 2019 (has links)
La teoría económica es un ambiente donde las matemáticas brindan muchos
aportes para modelizar comportamientos de agentes económicos. En este contexto,
la presente tesis enfatiza el despliegue matemático para tratar el problema
del consumidor en una economía descrita por bienes de consumo. Estos conforman
canastas de consumo que son identi ficados con elementos de un cono
convexo de un espacio vectorial apropiado como es el caso estándar de Rn, y
por un sistema de precios, los cuales son identi ficados con vectores del cono
dual topológico asociado al cono de las canastas de consumo. El problema del
consumidor, es un modelo en el que un consumidor elige canastas de bienes (los
cuales son accesibles para él considerando su restricción presupuestaria) de tal
forma que maximice su satisfacción por el consumo de estas. El problema del
consumidor se puede formular desde dos perspectivas distintas, ya sea mediante
preferencias o mediante funciones de utilidad que representan la satisfacción del
agente. En ambas formulaciones la solución al problema del consumidor es un
conjunto de canastas de bienes dando lugar a una aplicación que asigna a cada
vector de precios un conjunto de canastas (puede ser vacío, unitario o de varios
elementos), a esta aplicación se le denomina correspondencia de demanda. En el
presente trabajo se realiza una exposición pormenorizada de la monotonicidad
de la correspondencia de demanda, vía preferencias y vía funciones de utilidad,
tomando en cuenta condiciones de diferenciabilidad así como de no diferenciabilidad
en lo que concierne a las funciones de utilidad. En algunos casos se debilita
la clásica condición de concavidad para la función de utilidad. Asimismo, se evidencia
el papel que juega la función de utilidad indirecta en el tratamiento de
la monotonicidad de la función de demanda. / Economic theory is an environment where mathematics provides many contributions
to model the behavior of economic agents. In this context, this thesis
emphasizes the mathematical deployment to deal with the problem of the consumer
in an economy described by consumer goods. These form bundles of
consumption that are identi ed with elements of a convex cone of an appropriate
vector space as is the standard case of Rn, and by a price system, which are
identi ed with vectors of the topological dual cone associated with the cone of
the bundles of consumption. The problem of the consumer, is a model in which
a consumer chooses bundles of goods (which are accessible to him considering
his budget constraint) in such a way that maximizes his satisfaction for the consumption
of these. The consumer problem can be formulated from two di erent
perspectives, either through preferences or through utility functions that represent
the agent's satisfaction. In both formulations the solution to the problem
of the consumer is a set of bundles of goods giving rise to an application that
assigns to each price vector a set of bundles (it can be empty, unitary or of
several elements), this application is called correspondence of demand. In the
present work a detailed exposition is made of the monotonicity of the correspondence
of demand, through preferences and through utility functions, taking
into account conditions of di erentiability as well as non-di erentiability with
respect to utility functions. In some cases the classic concavity condition for
the utility function is weakened. Likewise, the role played by the indirect utility
function in the treatment of the monotonicity of the demand function is evident. / Tesis
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