Publicación: Anticipating Stochastic Integration
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2019-07-11
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Atribución-NoComercial-SinDerivadas 4.0 Internacional
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Universidad Nacional de Educación a Distancia (España). Facultad de Ciencias
Resumen
En esta tesis, se estudia la teoría de integración estocástica de Itô, así como, su aplicación en la modelización financiera a partir de las ecuaciones diferenciales estocásticas. A continuación, se presentan dos nuevas teorías de integración, la integral estocástica de Ayed-Kuo y la de Russo-Vallois, que generalizan la de Itô en el sentido de que introducen el cálculo estocástico anticipante. Se analizan algunas de sus propiedades más importantes, así como sus respectivas extensiones de la formula de Itô. Finalmente, se transponen ambas integrales a la teoría de ecuaciones diferenciales estocásticas y se introduce el problema de inversión con información privilegiada, cuyas hipotésis están relacionadas con la condición anticipante. Para este último punto, se proponen dos nuevos teoremas que se han demostrado en este trabajo.
In this thesis, the Itô theory of stochastic integration is studied, as well as its application in financial modeling based on stochastic differential equations. Then, two new integration theories are presented, the Ayed-Kuo and the Russo-Vallois stochastic integrals, which generalize the Itô one in the sense that they deal with anticipating stochastic calculus. Some of their most remarkable properties are discussed, as well as their respectively extensions of the Itô formula. Finally, both integrals are transposed to the stochastic differential equations theory and the insider trading problem is introduced, whose hypothesis are related to the anticipating condition. For this final point, two new theorems, which have been proved in this work, are proposed.
In this thesis, the Itô theory of stochastic integration is studied, as well as its application in financial modeling based on stochastic differential equations. Then, two new integration theories are presented, the Ayed-Kuo and the Russo-Vallois stochastic integrals, which generalize the Itô one in the sense that they deal with anticipating stochastic calculus. Some of their most remarkable properties are discussed, as well as their respectively extensions of the Itô formula. Finally, both integrals are transposed to the stochastic differential equations theory and the insider trading problem is introduced, whose hypothesis are related to the anticipating condition. For this final point, two new theorems, which have been proved in this work, are proposed.
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Categorías UNESCO
Palabras clave
Brownian motion, Itô Stochastic Integration, stochastic differential equations, anticipating stochastic calculus, Ayed-Kuo integral, Russo-Vallois integral, insider trading
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Facultad de Ciencias
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Estadística, Investigación Operativa y Cálculo Numérico