Matemáticas Aplicadas

URI permanente para esta colecciónhttp://54.81.141.168/handle/123456789/9101

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Temasearch.filters.applied.operator.equals: search.filters.subject.Finanzas--Modelos matemáticos

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    Representación dual de medidas de riesgo de valor conjunto
    (Pontificia Universidad Católica del Perú, 2021-02-26) Sinche Chocca, Nildo; Jordán Liza, Abelardo
    En las últimas décadas se ha desarrollado la construcción de una teoría matemática, de base probabilística, sobre las medidas de riesgo, debido a la necesidad de administrar el riesgo de una posición financiera. En la presente tesis se hace una presentación exhaustiva de las medidas de riesgo de valor conjunto, conjuntos de aceptación y la conexión biunívoca entre ellas. Luego, se expone de manera rigurosa una representación dual de las medidas de riesgo de valor conjunto. Con esa finalidad, se despliegan las herramientas necesarias como el análisis convexo de las aplicaciones de valor conjunto.
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    Selección de portafolio bajo el enfoque media-varianza y con cambio de régimen
    (Pontificia Universidad Católica del Perú, 2019-06-27) Ramos Torres, Luis Martín; Farfán Vargas, Jonathan Samuel
    In the present work, we will study the portfolio selection problem under the meanvariance framework with regime switching. This regime switching is modeled by an homogeneous finite-state Markov chain and affects the relevant financial parameters, such as the appreciation rate and volatility of asset returns. The aim of the agent under study (for example, an investor, a bank, etc.) is to find a portfolio such that the risk of his terminal wealth is minimized while his expected terminal wealth is fixed at some acceptable level. We consider two situations of analysis: (I) A financial market without risk-free asset. Modeling the financial market in this way adds realism to the portfolio selection problem, especially for long-term investment horizons. In this case, we will formulate the mean-variance optimization problem and a feasibility theorem will be proved. Furthermore, we will derive the efficient portfolio and the efficient frontier in closed form. (II) A problem of asset-liability management. In this case, we will consider a financial market with risk-free asset and two relevant stochastic processes: the asset value process of the company and its liability value process. The goal of it is to obtain the surplus value process of the company, which is the difference between asset value and liability value. As in the previous case, we will formulate the mean-variance optimization problem and a feasibility theorem will be proved. Furthermore, we will derive the efficient portfolio and the efficient frontier in closed form.