English
Risk theory: models and objectives PDMPs in risk theory and QMC integration I
Virtualconference
Auteurs : Thonhauser, Stefan (Auteur de la conférence)
CIRM (Editeur )
60J25 - Continuous-time Markov processes on general state spaces
65R20 - Integral equations
91B30 - Risk theory, insurance
91G60 - Numerical methods in mathematical finance
Ressources complémentaires :
https://www.cirm-math.com/uploads/2/6/6/0/26605521/thonhauser_cirm_i.pdf
CIRM (Editeur )
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Résumé :
This talk will give an overview on the usage of piecewise deterministic Markov processes for risk theoretic modeling and the application of QMC integration in this framework. This class of processes includes several common risk models and their generalizations. In this field, many objects of interest such as ruin probabilities, penalty functions or expected dividend payments are typically studied by means of associated integro-differential equations. Unfortunately, only particular parameter constellations allow for closed form solutions such that in general one needs to rely on numerical methods. Instead of studying these associated integro-differential equations, we adapt the problem in a way that allows us to apply deterministic numerical integration algorithms such as QMC rules.
Mots-Clés : risk theory; Markov process; quasi Monte-Carlo integration
Codes MSC : Mots-Clés : risk theory; Markov process; quasi Monte-Carlo integration
60J25 - Continuous-time Markov processes on general state spaces
65R20 - Integral equations
91B30 - Risk theory, insurance
91G60 - Numerical methods in mathematical finance
Ressources complémentaires :
https://www.cirm-math.com/uploads/2/6/6/0/26605521/thonhauser_cirm_i.pdf
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de Publication : 02/11/2020 Date de Captation : 02/11/2020 Sous Collection : Research School Catégorie arXiv : Quantitative Finance ; Probability Domaine(s) : Probabilités & Statistiques Format : MP4 (.mp4) - HD Durée : 01:13:53 Audience : Chercheurs Download : https://videos.cirm-math.fr/2020-10-26_Thonhauser_1.mp4 
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Informations sur la Rencontre
Nom de la Rencontre : Jean-Morlet Chair 2020 - Research School: Quasi-Monte Carlo Methods and Applications / Chaire Jean-Morlet 2020 - Ecole: Méthode de quasi-Monte-Carlo et applicationsOrganisateurs de la Rencontre : Rivat, Joël ; Thonhauser, Stefan ; Tichy, Robert Dates : 02/11/2020 - 07/11/2020 Année de la rencontre : 2020 URL de la Rencontre : https://www.chairejeanmorlet.com/2255.html
Données de citation
DOI : 10.24350/CIRM.V.19664803Citer cette vidéo: Thonhauser, Stefan (2020). Risk theory: models and objectives PDMPs in risk theory and QMC integration I. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19664803 URI : http://dx.doi.org/10.24350/CIRM.V.19664803 |
Voir Aussi
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- [Virtualconference] Brief introduction of Quasi-Monte Carlo Methods and their Applications / Auteur de la conférence Leobacher, Gunther.
- [Virtualconference] Two concrete FinTech applications of QMC / Auteur de la conférence Larcher, Gerhard.
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Bibliographie
- KRITZER, Peter, LEOBACHER, Gunther, SZÖLGYENYI, Michaela, et al. Approximation methods for piecewise deterministic Markov processes and their costs. Scandinavian actuarial journal, 2019, vol. 2019, no 4, p. 308-335. - https://doi.org/10.1080/03461238.2018.1560357
- PREISCHL, Michael, THONHAUSER, Stefan, et TICHY, Robert F. Integral equations, quasi-monte carlo methods and risk modeling. In : Contemporary Computational Mathematics-A Celebration of the 80th Birthday of Ian Sloan. Springer, Cham, 2018. p. 1051-1074. - http://dx.doi.org/10.1007/978-3-319-72456-0_47
- PAUSINGER, Florian et SVANE, Anne Marie. A Koksma–Hlawka inequality for general discrepancy systems. Journal of Complexity, 2015, vol. 31, no 6, p. 773-797. - https://doi.org/10.1016/j.jco.2015.06.002
