Numerical computation of risk functionals in PDMP risk models

Lea Maria Enzi; Stefan Thonhauser

doi:10.1007/978-3-031-59762-6_10

Numerical computation of risk functionals in PDMP risk models

Lea Maria Enzi
, Stefan Thonhauser

Institute of Statistics (5060)

Research output: Chapter in Book/Report/Conference proceeding › Conference paper › peer-review

Abstract

We analyze the ruin event in a Markovian insurance risk model. For actual computations of risk functionals, we sketch different numerical approaches and focus on assessing the performance of a quantization algorithm. Since by nature ruin should be a rare event, it is necessary to deploy a variance reduction technique based on a proper change of measure.

Original language	English
Title of host publication	Monte Carlo and Quasi-Monte Carlo Methods - MCQMC 2022
Subtitle of host publication	MCQMC 2022, Linz, Austria
Editors	Aicke Hinrichs, Friedrich Pillichshammer, Peter Kritzer
Place of Publication	Cham
Publisher	Springer Nature Switzerland AG
Pages	223-240
Number of pages	18
ISBN (Print)	978-3-031-59761-9
DOIs	https://doi.org/10.1007/978-3-031-59762-6_10
Publication status	Published - 2024

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	460

Keywords

QMC integration
Quantization
Ruin theory

ASJC Scopus subject areas

Applied Mathematics
General Mathematics

Fields of Expertise

Information, Communication & Computing

Treatment code (Nähere Zuordnung)

Basic - Fundamental (Grundlagenforschung)

Access to Document

10.1007/978-3-031-59762-6_10

Cite this

Enzi, L. M., & Thonhauser, S. (2024). Numerical computation of risk functionals in PDMP risk models. In A. Hinrichs, F. Pillichshammer, & P. Kritzer (Eds.), Monte Carlo and Quasi-Monte Carlo Methods - MCQMC 2022: MCQMC 2022, Linz, Austria (pp. 223-240). (Springer Proceedings in Mathematics and Statistics; Vol. 460). Springer Nature Switzerland AG. https://doi.org/10.1007/978-3-031-59762-6_10

Numerical computation of risk functionals in PDMP risk models. / Enzi, Lea Maria; Thonhauser, Stefan.
Monte Carlo and Quasi-Monte Carlo Methods - MCQMC 2022: MCQMC 2022, Linz, Austria. ed. / Aicke Hinrichs; Friedrich Pillichshammer; Peter Kritzer. Cham: Springer Nature Switzerland AG, 2024. p. 223-240 (Springer Proceedings in Mathematics and Statistics; Vol. 460).

Research output: Chapter in Book/Report/Conference proceeding › Conference paper › peer-review

Enzi, LM & Thonhauser, S 2024, Numerical computation of risk functionals in PDMP risk models. in A Hinrichs, F Pillichshammer & P Kritzer (eds), Monte Carlo and Quasi-Monte Carlo Methods - MCQMC 2022: MCQMC 2022, Linz, Austria. Springer Proceedings in Mathematics and Statistics, vol. 460, Springer Nature Switzerland AG, Cham, pp. 223-240. https://doi.org/10.1007/978-3-031-59762-6_10

@inproceedings{8f59350f75974e52b25e4a4db2d9503a,

title = "Numerical computation of risk functionals in PDMP risk models",

abstract = "We analyze the ruin event in a Markovian insurance risk model. For actual computations of risk functionals, we sketch different numerical approaches and focus on assessing the performance of a quantization algorithm. Since by nature ruin should be a rare event, it is necessary to deploy a variance reduction technique based on a proper change of measure.",

keywords = "QMC integration, Quantization, Ruin theory",

author = "Enzi, \{Lea Maria\} and Stefan Thonhauser",

year = "2024",

doi = "10.1007/978-3-031-59762-6\_10",

language = "English",

isbn = "978-3-031-59761-9",

series = "Springer Proceedings in Mathematics and Statistics",

publisher = "Springer Nature Switzerland AG",

pages = "223--240",

editor = "Aicke Hinrichs and Friedrich Pillichshammer and Peter Kritzer",

booktitle = "Monte Carlo and Quasi-Monte Carlo Methods - MCQMC 2022",

address = "Switzerland",

}

TY - GEN

T1 - Numerical computation of risk functionals in PDMP risk models

AU - Enzi, Lea Maria

AU - Thonhauser, Stefan

PY - 2024

Y1 - 2024

N2 - We analyze the ruin event in a Markovian insurance risk model. For actual computations of risk functionals, we sketch different numerical approaches and focus on assessing the performance of a quantization algorithm. Since by nature ruin should be a rare event, it is necessary to deploy a variance reduction technique based on a proper change of measure.

AB - We analyze the ruin event in a Markovian insurance risk model. For actual computations of risk functionals, we sketch different numerical approaches and focus on assessing the performance of a quantization algorithm. Since by nature ruin should be a rare event, it is necessary to deploy a variance reduction technique based on a proper change of measure.

KW - QMC integration

KW - Quantization

KW - Ruin theory

UR - https://www.scopus.com/pages/publications/85200685384

U2 - 10.1007/978-3-031-59762-6_10

DO - 10.1007/978-3-031-59762-6_10

M3 - Conference paper

SN - 978-3-031-59761-9

T3 - Springer Proceedings in Mathematics and Statistics

SP - 223

EP - 240

BT - Monte Carlo and Quasi-Monte Carlo Methods - MCQMC 2022

A2 - Hinrichs, Aicke

A2 - Pillichshammer, Friedrich

A2 - Kritzer, Peter

PB - Springer Nature Switzerland AG

CY - Cham

ER -

Numerical computation of risk functionals in PDMP risk models

Abstract

Publication series

Keywords

ASJC Scopus subject areas

Fields of Expertise

Treatment code (Nähere Zuordnung)

Access to Document

Other files and links

FWF - Risk Modelling - Analysis, Simulation and Optimization

Cite this

Numerical computation of risk functionals in PDMP risk models

Abstract

Publication series

Keywords

ASJC Scopus subject areas

Fields of Expertise

Treatment code (Nähere Zuordnung)

Access to Document

Other files and links

Projects

FWF - Risk Modelling - Analysis, Simulation and Optimization

Cite this