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Risk theory: models and objectives PDMPs in risk theory and QMC integration I
Virtualconference
Authors : Thonhauser, Stefan (Author of the conference)
CIRM (Publisher )
60J25 - Continuous-time Markov processes on general state spaces
65R20 - Integral equations
91B30 - Risk theory, insurance
91G60 - Numerical methods in mathematical finance
Additional resources :
https://www.cirm-math.com/uploads/2/6/6/0/26605521/thonhauser_cirm_i.pdf
CIRM (Publisher )
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Abstract :
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.
Keywords : risk theory; Markov process; quasi Monte-Carlo integration
MSC Codes : Keywords : 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
Additional resources :
https://www.cirm-math.com/uploads/2/6/6/0/26605521/thonhauser_cirm_i.pdf
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 02/11/2020 Conference Date : 02/11/2020 Subseries : Research School arXiv category : Quantitative Finance ; Probability Mathematical Area(s) : Probability & Statistics Format : MP4 (.mp4) - HD Video Time : 01:13:53 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2020-10-26_Thonhauser_1.mp4 
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Information on the Event
Event Title : Jean-Morlet Chair 2020 - Research School: Quasi-Monte Carlo Methods and Applications / Chaire Jean-Morlet 2020 - Ecole: Méthode de quasi-Monte-Carlo et applicationsEvent Organizers : Rivat, Joël ; Thonhauser, Stefan ; Tichy, Robert Dates : 02/11/2020 - 07/11/2020 Event Year : 2020 Event URL : https://www.chairejeanmorlet.com/2255.html
Citation Data
DOI : 10.24350/CIRM.V.19664803Cite this video as: 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 |
See Also
- [Virtualconference] PDMPs in risk theory and QMC integration III / Author of the conference Thonhauser, Stefan.
- [Virtualconference] On the estimation of conditional quantiles - lecture 3 / Author of the conference Maume-Deschamps, Véronique.
- [Virtualconference] On the estimation of conditional quantiles - lecture 2 / Author of the conference Maume-Deschamps, Véronique.
- [Virtualconference] Stochastic differential equations / Author of the conference Leobacher, Gunther.
- [Virtualconference] Number sequences for simulation - lecture 2 / Author of the conference Ökten, Giray.
- [Virtualconference] PDMPs and Integrals PDMPs in risk theory and QMC integration II / Author of the conference Thonhauser, Stefan.
- [Virtualconference] Derivative pricing, simulation from non-uniform distributions - lecture 3 / Author of the conference Ökten, Giray.
- [Multi angle] Quasi-Monte Carlo methods and applications: introduction / Author of the conference Tichy, Robert.
- [Virtualconference] The coordinate sampler: a non-reversible Gibbs-like MCMC sampler / Author of the conference Robert, Christian P.
- [Virtualconference] On the estimation of conditional quantiles - lecture 1 / Author of the conference Maume-Deschamps, Véronique.
- [Virtualconference] Brief introduction of Quasi-Monte Carlo Methods and their Applications / Author of the conference Leobacher, Gunther.
- [Virtualconference] Two concrete FinTech applications of QMC / Author of the conference Larcher, Gerhard.
- [Virtualconference] Number sequences for simulation - lecture 1 / Author of the conference Ökten, Giray.
- [Virtualconference] Optimizing dividends and limited capital injections via exponential approximations I / Author of the conference Avram, Florin.
Bibliography
- 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
