Modelo de Contagio Dinámico: una aplicación al problema de la ruina. (Dynamic Contagion Model a Ruin Problem)
diagramas, ilustraciones, tablas
- Autores:
-
Rueda Corredor, Henry Steven
- Tipo de recurso:
- Fecha de publicación:
- 2021
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/79627
- Palabra clave:
- 330 - Economía
Riesgo
Risk
Modelo de Contagio Dinámico
Probabilidad de Ruina
Teoría de Ruina
Proceso de Hawkes
Apiñamiento Puntual
Proceso de Contagio Dinámico
Modelos de Riesgo tipo Erlang
Administradora de Riesgos Laborales (ARL)
Dynamic Contagion Model
Ruin Probability
Erlang Risk Models
Cluster Point Process
Teoría económica
Economic theory
- Rights
- openAccess
- License
- Atribución-NoComercial-SinDerivadas 4.0 Internacional
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| dc.title.none.fl_str_mv |
Modelo de Contagio Dinámico: una aplicación al problema de la ruina. (Dynamic Contagion Model a Ruin Problem) |
| dc.title.translated.eng.fl_str_mv |
Dynamic Contagion Model: an application to the ruin problem |
| title |
Modelo de Contagio Dinámico: una aplicación al problema de la ruina. (Dynamic Contagion Model a Ruin Problem) |
| spellingShingle |
Modelo de Contagio Dinámico: una aplicación al problema de la ruina. (Dynamic Contagion Model a Ruin Problem) 330 - Economía Riesgo Risk Modelo de Contagio Dinámico Probabilidad de Ruina Teoría de Ruina Proceso de Hawkes Apiñamiento Puntual Proceso de Contagio Dinámico Modelos de Riesgo tipo Erlang Administradora de Riesgos Laborales (ARL) Dynamic Contagion Model Ruin Probability Erlang Risk Models Cluster Point Process Teoría económica Economic theory |
| title_short |
Modelo de Contagio Dinámico: una aplicación al problema de la ruina. (Dynamic Contagion Model a Ruin Problem) |
| title_full |
Modelo de Contagio Dinámico: una aplicación al problema de la ruina. (Dynamic Contagion Model a Ruin Problem) |
| title_fullStr |
Modelo de Contagio Dinámico: una aplicación al problema de la ruina. (Dynamic Contagion Model a Ruin Problem) |
| title_full_unstemmed |
Modelo de Contagio Dinámico: una aplicación al problema de la ruina. (Dynamic Contagion Model a Ruin Problem) |
| title_sort |
Modelo de Contagio Dinámico: una aplicación al problema de la ruina. (Dynamic Contagion Model a Ruin Problem) |
| dc.creator.fl_str_mv |
Rueda Corredor, Henry Steven |
| dc.contributor.advisor.none.fl_str_mv |
Sánchez Vásquez, Alejandra |
| dc.contributor.author.none.fl_str_mv |
Rueda Corredor, Henry Steven |
| dc.subject.ddc.spa.fl_str_mv |
330 - Economía |
| topic |
330 - Economía Riesgo Risk Modelo de Contagio Dinámico Probabilidad de Ruina Teoría de Ruina Proceso de Hawkes Apiñamiento Puntual Proceso de Contagio Dinámico Modelos de Riesgo tipo Erlang Administradora de Riesgos Laborales (ARL) Dynamic Contagion Model Ruin Probability Erlang Risk Models Cluster Point Process Teoría económica Economic theory |
| dc.subject.other.none.fl_str_mv |
Riesgo Risk |
| dc.subject.proposal.spa.fl_str_mv |
Modelo de Contagio Dinámico Probabilidad de Ruina Teoría de Ruina Proceso de Hawkes Apiñamiento Puntual Proceso de Contagio Dinámico Modelos de Riesgo tipo Erlang Administradora de Riesgos Laborales (ARL) |
| dc.subject.proposal.eng.fl_str_mv |
Dynamic Contagion Model Ruin Probability Erlang Risk Models Cluster Point Process |
| dc.subject.unesco.none.fl_str_mv |
Teoría económica Economic theory |
| description |
diagramas, ilustraciones, tablas |
| publishDate |
2021 |
| dc.date.accessioned.none.fl_str_mv |
2021-06-11T16:23:07Z |
| dc.date.available.none.fl_str_mv |
2021-06-11T16:23:07Z |
| dc.date.issued.none.fl_str_mv |
2021 |
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Trabajo de grado - Maestría |
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info:eu-repo/semantics/masterThesis |
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info:eu-repo/semantics/acceptedVersion |
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Text |
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acceptedVersion |
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https://repositorio.unal.edu.co/handle/unal/79627 |
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Universidad Nacional de Colombia |
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Repositorio Institucional Universidad Nacional de Colombia |
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https://repositorio.unal.edu.co/ |
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https://repositorio.unal.edu.co/handle/unal/79627 https://repositorio.unal.edu.co/ |
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Universidad Nacional de Colombia Repositorio Institucional Universidad Nacional de Colombia |
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spa |
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spa |
| dc.relation.references.spa.fl_str_mv |
Albrecher, H., and Asmussen, S. Ruin probabilities and aggregrate claims distributions for shot noise cox processes. Scandinavian Actuarial Journal 2006 (03 2006). Blanco, L. Probabilidad, 1 ed. Universidad Nacional de Colombia, 2004. Chen, Z., Dassios, A., Kuan, V., Lim, J., Qu, Y., Surya, B., and Zhao, H. A two-phase dynamic contagion model for covid-19. SSRN Electronic Journal (06 2020). Cheng, Y.-J., Hou, M., and Wang, J. An improved optimal trigonometric elm algorithm for numerical solution to ruin probability of erlang(2) risk model. Multimedia Tools and Applications 79 (11 2020). Constantinescu, C., Samorodnitsky, G., and Zhu, W. Ruin probabilities in classical risk models with gamma claims. Scandinavian Actuarial Journal 2018 (11 2017). Dassios, A., and Jang, J.-W. Pricing of catastrophe reinsurance and derivatives using the cox process with shot noise intensity. Finance and Stochastics 7 (2003), 73-95. Dassios, A., and Zhao, H. A dynamic contagion process. Advances in Applied Probability 43 (09 2011). Dassios, A., and Zhao, H. A risk model with delayed claims. Journal of Applied Probability 1 (2013), 1-19. Dickson, D., and Li, S. The distributions of some quantities for erlang(2) risk models. 18. Hawkes, A. Point spectra of some mutually exciting point processes. Journal of the Royal Statistical Society. Series B 33 (07 1971). Hawkes, A., and Oakes, D. A cluster process representation of a self-exciting process. Journal of Applied Probability 11 (09 1974), 493-503. Ibe, O. Markov Processes for Stochastic Modeling, 1 ed. ELSEVIER, 1997. Jang, J., and Dassios, A. A bivariate shot noise hawkes process for insurance. SSRN Electronic Journal (05 2011). Jang, J., and Oh, R. A review on poisson, cox, hawkes, shot-noise poisson and dynamic contagion process and their compound processes. Annals of Actuarial Science (09 2020), 1-22. Li, S., and Garrido, J. On ruin for the erlang(n) risk process. Insurance: Mathematics and Economics 34 (06 2004), 391-408. Marmol, M., Claramunt, M. M., and Castañer, A. Aplicaciones de la transformada de laplace a la teoría del riesgo. Anales del Instituto de Actuarios Españoles (01 2007), 9-36. Dassios, A., Jang, J., and Zhao, H. A generalised cir process with externallyexciting and self-exciting jumps and its applications in insurance and finance. Risks 7 (10 2019), 103. Dassios, A., and Zhao, H. Effcient simulation of clustering jumps with cir intensity. Operations Research 65 (10 2017), 1494-1515. Dickson, D., and Li, S. Erlang risk models and finite time ruin problems. Scandinavian Actuarial Journal - SCAND ACTUAR J 2012 (01 2010), 1-20. Davis, M. H. A. Piecewise-deterministic markov processes: A general class of nondiffusion stochastic models. Journal of the Royal Statistical Society: Series B (Methodological) 46 (1984), 353-376. Masson, P. Contagion: Monsoonal effects, spillovers, and jumps between multiple equilibria. IMF Working Papers (1998), 1-32. Mikosch, T. Non-Life Insurance Mathematics. An Introduction with the Poisson Process, 2 ed. Springer, 2009. Moreno, L. G. Teoría del riesgo. apuntes de clase. 2016. Pasricha, P., and Selvamuthu, D. A markov modulated dynamic contagion process with application to credit risk. Journal of Statistical Physics 175 (04 2019). Puneet Pasricha, D. S. A markov modulated dynamic contagion process with application to credit risk. Journal of Statistical Physics 175 (2019), 495-511. Rincón, L. Introducción a la teoría del riesgo, 1 ed. UNAM, 2012. Stuart A. Klugman, Harry H. Panjer, G. E. W. LOSS MODELS. From Data to Decisions, 4 ed. John Wiley Sons, 2012. Zhao, H. A Dynamic Contagion Process for Modelling Contagion Risk in Finance and Insurance. PhD thesis, London School of Economics, 2012. |
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Atribución-NoComercial-SinDerivadas 4.0 Internacional |
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http://creativecommons.org/licenses/by-nc-nd/4.0/ |
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1 recurso en línea (67 páginas) |
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application/pdf |
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Universidad Nacional de Colombia |
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Bogotá - Ciencias - Maestría en Actuaría y Finanzas |
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Departamento de Matemáticas |
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Facultad de Ciencias |
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Bogotá |
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Universidad Nacional de Colombia - Sede Bogotá |
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Universidad Nacional de Colombia |
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Atribución-NoComercial-SinDerivadas 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Sánchez Vásquez, Alejandra3518fa270556b9b3645800be2f07ea31Rueda Corredor, Henry Steven25f1db99fc6c69a38ace42e35915bf192021-06-11T16:23:07Z2021-06-11T16:23:07Z2021https://repositorio.unal.edu.co/handle/unal/79627Universidad Nacional de ColombiaRepositorio Institucional Universidad Nacional de Colombiahttps://repositorio.unal.edu.co/diagramas, ilustraciones, tablasEste trabajo estudia el Modelo de Contagio Dinámico y sus propiedades, propuesto por Dassios y Zhao (2011) [8], el cual es una generalización de los procesos de Hawkes y los procesos doblemente estocásticos con intensidad de shot noise con el fin de representar situaciones de apiñamiento. Este proceso estocástico incluye los saltos externamente excitados y auto-excitados para modelar el impacto que pueden llegar a tener en el sistema factores tanto exógenos como endógenos. Por medio de este proceso se simuló la probabilidad de ruina de una compañía aseguradora cuando el tamaño de las reclamaciones sigue una distribución exponencial y una Erlang tipo 2. El objetivo principal de la tesis es demostrar que el modelo es útil para simular el valor que debe destinar una Administradora de Riesgos Laborales (ARL) para determinar el monto de la reserva que permita cubrir todos los procedimientos médicos futuros de un empleado cuyo siniestro es un accidente o enfermedad laboral en Colombia. Esta aproximación se hace desde los conceptos de la Teoría de la Ruina y por consiguiente, el superávit, la condición de ganancia neta y las cotas de la probabilidad de ruina, también son estudiadas. Finalmente, se da el primer acercamiento al cálculo de la reserva para un portafolio de n empleados asegurados.This paper will focus on the study of the Dynamic Contagion Model and its properties, proposed by Dassios and Zhao (2011) [8], which is a generalisation of Hawkes processes and doubly stochastic processes with intensity of shot noise in order to model clustering situations. This stochastic process includes externally-excited and self-excited jumps to model both exogenous and endogenous factors impact on the underlying system. Through this process, we simulated the probability of ruin of an insurance company when the size of claims follows an exponential and an Erlang type 2 distribution. The aim of the thesis is to demonstrate that the model is useful to simulate the value that a professional risk managers must allocate to determine the amount of the reserve that allows to cover all the future medical procedures of an employee whose claim is an accident or occupational disease in Colombia. This approach is based on the concepts of the Theory of Ruin and, consequently, the surplus, the net profit condition and the probability of ruin are also studied. Finally, the first approach to the calculation of the reserve for a portfolio of n insured employees is also given.MaestríaMagíster en Actuaría y Finanzas1 recurso en línea (67 páginas)application/pdfspaUniversidad Nacional de ColombiaBogotá - Ciencias - Maestría en Actuaría y FinanzasDepartamento de MatemáticasFacultad de CienciasBogotáUniversidad Nacional de Colombia - Sede Bogotá330 - EconomíaRiesgoRiskModelo de Contagio DinámicoProbabilidad de RuinaTeoría de RuinaProceso de HawkesApiñamiento PuntualProceso de Contagio DinámicoModelos de Riesgo tipo ErlangAdministradora de Riesgos Laborales (ARL)Dynamic Contagion ModelRuin ProbabilityErlang Risk ModelsCluster Point ProcessTeoría económicaEconomic theoryModelo de Contagio Dinámico: una aplicación al problema de la ruina. (Dynamic Contagion Model a Ruin Problem)Dynamic Contagion Model: an application to the ruin problemTrabajo de grado - Maestríainfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/acceptedVersionTexthttp://purl.org/redcol/resource_type/TMAlbrecher, H., and Asmussen, S. Ruin probabilities and aggregrate claims distributions for shot noise cox processes. Scandinavian Actuarial Journal 2006 (03 2006).Blanco, L. Probabilidad, 1 ed. Universidad Nacional de Colombia, 2004.Chen, Z., Dassios, A., Kuan, V., Lim, J., Qu, Y., Surya, B., and Zhao, H. A two-phase dynamic contagion model for covid-19. SSRN Electronic Journal (06 2020).Cheng, Y.-J., Hou, M., and Wang, J. An improved optimal trigonometric elm algorithm for numerical solution to ruin probability of erlang(2) risk model. Multimedia Tools and Applications 79 (11 2020).Constantinescu, C., Samorodnitsky, G., and Zhu, W. Ruin probabilities in classical risk models with gamma claims. Scandinavian Actuarial Journal 2018 (11 2017).Dassios, A., and Jang, J.-W. Pricing of catastrophe reinsurance and derivatives using the cox process with shot noise intensity. Finance and Stochastics 7 (2003), 73-95.Dassios, A., and Zhao, H. A dynamic contagion process. Advances in Applied Probability 43 (09 2011).Dassios, A., and Zhao, H. A risk model with delayed claims. Journal of Applied Probability 1 (2013), 1-19.Dickson, D., and Li, S. The distributions of some quantities for erlang(2) risk models. 18.Hawkes, A. Point spectra of some mutually exciting point processes. Journal of the Royal Statistical Society. Series B 33 (07 1971).Hawkes, A., and Oakes, D. A cluster process representation of a self-exciting process. Journal of Applied Probability 11 (09 1974), 493-503.Ibe, O. Markov Processes for Stochastic Modeling, 1 ed. ELSEVIER, 1997.Jang, J., and Dassios, A. A bivariate shot noise hawkes process for insurance. SSRN Electronic Journal (05 2011).Jang, J., and Oh, R. A review on poisson, cox, hawkes, shot-noise poisson and dynamic contagion process and their compound processes. Annals of Actuarial Science (09 2020), 1-22.Li, S., and Garrido, J. On ruin for the erlang(n) risk process. Insurance: Mathematics and Economics 34 (06 2004), 391-408.Marmol, M., Claramunt, M. M., and Castañer, A. Aplicaciones de la transformada de laplace a la teoría del riesgo. Anales del Instituto de Actuarios Españoles (01 2007), 9-36.Dassios, A., Jang, J., and Zhao, H. A generalised cir process with externallyexciting and self-exciting jumps and its applications in insurance and finance. Risks 7 (10 2019), 103.Dassios, A., and Zhao, H. Effcient simulation of clustering jumps with cir intensity. Operations Research 65 (10 2017), 1494-1515.Dickson, D., and Li, S. Erlang risk models and finite time ruin problems. Scandinavian Actuarial Journal - SCAND ACTUAR J 2012 (01 2010), 1-20.Davis, M. H. A. Piecewise-deterministic markov processes: A general class of nondiffusion stochastic models. Journal of the Royal Statistical Society: Series B (Methodological) 46 (1984), 353-376.Masson, P. Contagion: Monsoonal effects, spillovers, and jumps between multiple equilibria. IMF Working Papers (1998), 1-32.Mikosch, T. Non-Life Insurance Mathematics. An Introduction with the Poisson Process, 2 ed. Springer, 2009.Moreno, L. G. Teoría del riesgo. apuntes de clase. 2016.Pasricha, P., and Selvamuthu, D. A markov modulated dynamic contagion process with application to credit risk. Journal of Statistical Physics 175 (04 2019).Puneet Pasricha, D. S. A markov modulated dynamic contagion process with application to credit risk. Journal of Statistical Physics 175 (2019), 495-511.Rincón, L. Introducción a la teoría del riesgo, 1 ed. UNAM, 2012.Stuart A. Klugman, Harry H. Panjer, G. E. W. LOSS MODELS. From Data to Decisions, 4 ed. John Wiley Sons, 2012.Zhao, H. A Dynamic Contagion Process for Modelling Contagion Risk in Finance and Insurance. PhD thesis, London School of Economics, 2012.LICENSElicense.txtlicense.txttext/plain; charset=utf-83964https://repositorio.unal.edu.co/bitstream/unal/79627/1/license.txtcccfe52f796b7c63423298c2d3365fc6MD51ORIGINAL1010204725.2021.pdf1010204725.2021.pdfTesis de Maestría en Actuaría y Finanzasapplication/pdf1816647https://repositorio.unal.edu.co/bitstream/unal/79627/2/1010204725.2021.pdf3763d625917e24fd2be3124722859a6dMD52CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8805https://repositorio.unal.edu.co/bitstream/unal/79627/3/license_rdf4460e5956bc1d1639be9ae6146a50347MD53THUMBNAIL1010204725.2021.pdf.jpg1010204725.2021.pdf.jpgGenerated Thumbnailimage/jpeg4699https://repositorio.unal.edu.co/bitstream/unal/79627/4/1010204725.2021.pdf.jpg1f21f694f394982a09a6f3fd88d1807bMD54unal/79627oai:repositorio.unal.edu.co:unal/796272024-07-22 00:38:38.697Repositorio Institucional Universidad Nacional de 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