Modeling continuous-time financial markets with capital gains taxes

We formulate a model of continuous-time financial market consisting of a bank account with constant interest rate and one risky asset subject to capital gains taxes. We consider the problem of maximizing expected utility from future consumption in infinite horizon. This is the continuous-time version of the model introduced by Dammon, Spatt and Zhang [11]. The taxation rule is linear so that it allows for tax credits when capital gains losses are experienced. In this context, wash sales are optimal. Our main contribution is to derive lower and upper bounds on the value function in terms of the corresponding value in a tax-free and frictionless model. While the upper bound corresponds to the value function in a tax-free model, the lower bound is a consequence of wash sales. As an important implication of these bounds, we derive an explicit first order expansion of our value function for small interest rate and tax rate coefficients. In order to examine the accuracy of this approximation, we provide a characterization of the value function in terms of the associated dynamic programming equation, and we suggest a numerical approximation scheme based on finite differences and the Howard algorithm. The numerical results show that the first order Taylor expansion is reasonably accurate for reasonable market data

Optimal Carbon Sequestration Policies in Leaky Reservoirs

We study in this report a model of optimal Carbon Capture and Storage in which the reservoir of sequestered carbon is leaky, and pollution eventually is released into the atmosphere. We formulate the social planner problem as an optimal control program and we describe the optimal consumption paths as a function of the initial conditions, the physical constants and the economical parameters. In particular, we show that the presence of leaks may lead to situations which do not occur otherwise, including that of non-monotonous price paths for the energy

Cuatro ensayos sobre valoración de derivados y estrategias de inversión

En esta tesis estudiaremos modelos empleados en la valoración de derivados financieros. Usaremos dos clases de técnicas de valoración, Réplica e Indifference Pricing. Abordaremos el problema de valoración en tiempo real, el de valoración de opciones con tipos de interés variable y los de inversión óptima y valoración de opciones bajo costes de transacción. Diseñaremos un método numérico que puede ser aplicado a diversos modelos o tipos de derivado y es capaz de valorar opciones o calibrar los parámetros del modelo de una o varias acciones. Realizaremos un estudio sobre cómo los tipos de interés variables se pueden incorporar a los modelos. Otro objetivo es, bajo un escenario con costes proporcionales de transacción, aplicar métodos espectrales a dos de las funciones de Utilidad más habituales: Potencial y Exponencial. Trabajaremos en el problema de Inversión Óptima bajo Utilidad Potencial y con el problema de valoración de opciones bajo Utilidad Exponencial.Departamento de Matemática Aplicad