Quantitative Risk Management under the Interplay of Insurance and Financial Risks
| dc.contributor.advisor | Tang, Qihe | spa |
| dc.contributor.advisor | Londoño Londoño, Jaime Alberto | spa |
| dc.contributor.author | Gómez De Los Ríos, Fabio Andrés | spa |
| dc.date.accessioned | 2020-02-25T20:20:05Z | spa |
| dc.date.available | 2020-02-25T20:20:05Z | spa |
| dc.date.issued | 2020-02 | spa |
| dc.description.abstract | En esta tesis, abordamos algunos problemas relacionados con la interacción de los riesgos de seguros y financieros. Primero, consideramos una compañía de seguros o financiera con la intención de asignar el capital de riesgo retenido para su cartera de inversión general entre sus constituyentes. Brevemente, suponemos que la compañía calcula el capital de riesgo a través de la medida de riesgo Haezendonck - Goovaerts, y establecemos la regla de asignación de capital única consistente con un enfoque RORAR (retorno sobre capital ajustado al riesgo). Además, presentamos algunas asintóticas y proponemos un estimador consistente para la regla de asignación de capital. Finalmente, realizamos algunos estudios numéricos. Luego, resolvemos el problema de valorar algunos derivados vinculados a la mortalidad empleando el enfoque de precios de indiferencia de utilidad. De manera sucinta, suponemos que el riesgo de mortalidad emana de una cartera de asegurados de vida, cuyas vidas restantes se modelan como tiempos aleatorios condicionalmente independientes. Al adaptar algunos resultados de la teoría del riesgo de crédito, calculamos una expresión explícita para el precio de indiferencia de la utilidad cuando el derivado es una combinación lineal de dotaciones puras. Al considerar una reclamación contingente más general, utilizamos técnicas de ecuaciones diferenciales estocásticas hacia atrás (BSDE) para caracterizar el precio de indiferencia en términos de una solución a un BSDE no lineal con un generador no Lipschitz. Finalmente, consideramos a un individuo con el objetivo de elegir de manera óptima sus estrategias de inversión, consumo y compra de seguros de vida en un mercado financiero completo. Al suponer que el criterio de optimización es la maximización de la utilidad esperada del individuo, la cual depende del estado de la economía, resolvemos el problema de elección óptima en una configuración general, que incluye varias funciones de utilidad empleadas en la literatura. | spa |
| dc.description.abstract | In this thesis, we tackle some problems concerning the interplay of insurance and financial risks. First, we consider an insurance or financial company intending to allocate the risk capital withheld for its overall investment portfolio among its constituents. Shortly, we assume that the company computes the risk capital through the Haezendonck--Goovaerts risk measure, and we establish the unique capital allocation rule consistent with a RORAR (return on risk-adjusted capital) approach. Besides, we present some asymptotics and propose a consistent estimator for the capital allocation rule. Finally, we conduct some numerical studies. Then, we solve the problem of valuing some mortality-linked derivatives by employing the utility indifference pricing approach. Succinctly, we suppose that the mortality risk emanates from a portfolio of life insurance policyholders, whose remaining lifetimes are modeled as conditionally independent random times. By adapting some results from credit risk theory, we compute an explicit expression for the utility indifference price when the derivative is a linear combination of pure endowments. By considering a more general contingent claim, we use techniques of backward stochastic differential equations (BSDE) to characterize the indifference price in terms of a solution to a non-linear BSDE with a non-Lipschitz generator. Finally, we consider an individual aiming to optimally choose its investment, consumption, and life insurance purchase strategies in a complete financial market. By assuming that the optimality criterion is the maximization of the individual's expected state-dependent utility, we solve the optimal choice problem in a general setup, which includes several utility functions employed in the literature. | spa |
| dc.description.additional | Doctor en Ciencia | spa |
| dc.description.degreelevel | Doctorado | spa |
| dc.format.extent | 107 | spa |
| dc.format.mimetype | application/pdf | spa |
| dc.identifier.uri | https://repositorio.unal.edu.co/handle/unal/75741 | |
| dc.language.iso | eng | spa |
| dc.publisher.branch | Universidad Nacional de Colombia - Sede Bogotá | spa |
| dc.publisher.department | Departamento de Matemáticas | spa |
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An economic approach to capital allocation. Journal of Risk and Insurance, 77(3), pp.523-549. | spa |
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| dc.rights.license | Atribución-NoComercial-SinDerivadas 4.0 Internacional | spa |
| dc.rights.spa | Acceso abierto | spa |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | spa |
| dc.subject.ddc | Matemáticas::Probabilidades y matemáticas aplicadas | spa |
| dc.subject.proposal | financial risks | spa |
| dc.subject.proposal | variables | spa |
| dc.subject.proposal | Quantitative | spa |
| dc.subject.proposal | Insurance | spa |
| dc.title | Quantitative Risk Management under the Interplay of Insurance and Financial Risks | spa |
| dc.title.alternative | Quantitative Risk Management under the Interplay of Insurance and Financial Risks | spa |
| dc.type | Trabajo de grado - Doctorado | spa |
| dc.type.coar | http://purl.org/coar/resource_type/c_db06 | spa |
| dc.type.coarversion | http://purl.org/coar/version/c_ab4af688f83e57aa | spa |
| dc.type.content | Text | spa |
| dc.type.driver | info:eu-repo/semantics/doctoralThesis | spa |
| dc.type.version | info:eu-repo/semantics/acceptedVersion | spa |
| oaire.accessrights | http://purl.org/coar/access_right/c_abf2 | spa |