Advanced search
Publication Cover
Stochastic Models Volume 36, 2020 - Issue 4
Submit an article Journal homepage
178
Views
5
CrossRef citations to date
0
Altmetric
Articles

Ruin probabilities for risk processes in a bipartite network

Anita BehmeInstitut für Mathematische Stochastik, Technische Universität Dresden, Dresden, Germany; ORCID Iconhttp://orcid.org/0000-0002-9999-7589
ORCID Icon,
Claudia KlüppelbergCenter for Mathematical Sciences, Technical University of Munich, Garching, Germany; Correspondence[email protected]
ORCID Iconhttp://orcid.org/0000-0002-0189-2384
ORCID Icon &
Gesine ReinertDepartment of Statistics, University of Oxford, Oxford, UKORCID Iconhttp://orcid.org/0000-0002-0363-9470
ORCID Icon
Pages 548-573 | Received 01 Aug 2019, Accepted 21 Apr 2020, Published online: 13 May 2020

References

  • Asmussen, S. Applied Probability and Queues; Springer, New York, 2nd ed., 2003.
  • Asmussen, S.; Albrecher, H.; Ruin Probabilities; World Scientific, Singapore, 2nd ed., 2010.
  • Avram, F.; Palmowski, Z.; Pistorius, M. Exit problem of a two-dimensional risk process from the quadrant: exact and asymptotic results. Ann. Appl. Probab. 2008, 18, 2421–2449. DOI: 10.1214/08-AAP529.
  • Avram, F.; Palmowski, Z.; Pistorius, M. A two-dimensional ruin problem on the positive quadrant. Insur Math Econ. 2008, 42, 227–234. DOI: 10.1016/j.insmatheco.2007.02.004.
  • Barbour, A.D.; Holst, L.; and S. Janson, Poisson Approximation; Oxford University Press, Oxford, 1992.
  • Bollobas, B.; Janson, S.; Riordan, O. The phase transition in inhomogeneous random graphs. Random Struct. Alg. 2007, 31, 3–122. DOI: 10.1002/rsa.20168.
  • Bregman, Y.; Klüppelberg, C. Ruin estimation in multivariate models with Clayton dependence structure. Scand. Act. J. 2005, 2005, 462–480. DOI: 10.1080/03461230500362065.
  • Chao, M. T.; Strawderman, W. E. Negative moments of positive random variables. JASA 1972, 67, 429–431. DOI: 10.1080/01621459.1972.10482404.
  • Collamore, J. F. First passage times of general sequences of random vectors: a large deviations approach. Stoch. Proc. Appl 1998, 78, 97–130. DOI: 10.1016/S0304-4149(98)00056-8.
  • Embrechts, P.; Klüppelberg, C.; and T. Mikosch, Modelling Extremal Events for Insurance and Finance; Springer, Heidelberg, 1997.
  • Kley, O.; Klüppelberg, C.; Reinert, G. Systemic risk in a large claims insurance market with bipartite graph structure. Oper. Res. 2016, 64, 1159–1176. DOI: 10.1287/opre.2016.1502.
  • Kley, O.; Klüppelberg, C.; Reinert, G. Conditional risk measures in a bipartite market structure. Scand. Act. J. 2018, 2018, 328–355. DOI: 10.1080/03461238.2017.1350203.
  • International Association of Insurance Supervisors (IAIS). Insurance and financial stability, 2011. Available at https://www.iaisweb.org/page/news/other-papers-and-reports//file/34041/insurance-and-financial-stability.
  • Pan, Y.; Borovkov, K. The exact asymptotics of the large deviation probabilities in the multivariate boundary crossing problem. Adv. Appl. Probab. 2019, 51, 835–864. DOI: 10.1017/apr.2019.28.
  • Ramasubramannian, S. Multidimensional ruin problem. Commun. Stoch. Anal. 2012, 6, 33–47.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.