121
Views
0
CrossRef citations to date
0
Altmetric
Research Article

Backward simulation of multivariate mixed Poisson processes

ORCID Icon, ORCID Icon &
Pages 3549-3572 | Received 16 Sep 2020, Accepted 11 Jun 2021, Published online: 01 Jul 2021

References

  • Aue F, Kalkbrener M. LDA at work: Deutsche Bank's approach to quantifying operational risk. J Oper Risk. 2006;1(4):49–93.
  • Bae T, Kreinin A. A backward construction and simulation of correlated Poisson processes. J Stat Comput Simul. 2017;87(8):1593–1607. Available from: https://doi.org/https://doi.org/10.1080/00949655.2016.1277428
  • Barndorff-Nielsen O, Shephard N. Non-Gaussian Ornstein–Uhlenbeck-based models and some of their uses in financial economics. J R Stat Soc Ser B. 2001;63(2):167–241.
  • Barndorff-Nielsen O, Yeo GF. Negative binomial processes. J Appl Probab. 1969;6(3):633–647.
  • Böcker K, Klüppelberg C. Multivariate models for operational risk. Quant Finance. 2010;10(8):855–869.
  • Chavez-Demoulin V, Embrechts P, Nešlehová J. Quantitative models for operational risk: extremes, dependence and aggregation. J Bank Finance. 2006;30(10):2635–2658.
  • Embrechts P, Puccetti G. Aggregating risk capital, with an application to operational risk. Geneva Risk Insurance Rev. 2006;31(2):71–90.
  • Panjer HH. Operational risk: modeling analytics. Hoboken, NJ: John Wiley & Sons; 2006.
  • Peters G, Shevchenko P, Wuthrich M. Dynamic operational risk: modeling dependence and combining different sources of information. J Oper Risk. 2009;4(2):69–104.
  • Shevchenko P. Modelling operational risk using Bayesian inference. Berlin, Heidelberg: Springer Science & Business Media; 2011.
  • Duch K, Kreinin A, Jiang Y. New approaches to operational risk modeling. IBM J Res Dev. 2014;3:31–45.
  • Lindskog F, McNeil AJ. Common Poisson shock models: applications to insurance and credit risk modelling. ASTIN Bull. 2003;33(2):209–238.
  • Nešlehová J, Embrechts P, Chavez-Demoulin V. Infinite mean models and the LDA for operational risk. J Oper Risk. 2006;1(1):3–25.
  • Powojowski M, Reynolds D, Tuenter H. Dependent events and operational risk. Algo Res Quart. 2002;5(2):65–73.
  • Griffiths RC, Milne RK, Wood R. Aspects of correlation in bivariate Poisson distributions and processes. Aust N Z J Stat. 1979;21(3):238–255.
  • Nelsen R. Discrete bivariate distributions with given marginals and correlation. Commun Stat Simul Comput. 1987;16(1):199–208.
  • Kreinin A. Correlated Poisson processes and their applications in financial modeling. In: Akansu AN, Kulkarni SR, Malioutov DM, editors. Financial signal processing and machine learning. John Wiley & Sons; 2016. Chapter 9; p. 191–230.
  • Fréchet M. Sur les tableaux de corrélation dont les marges sont données. Rev Inst Int Statist. 1951;14:53–77.
  • Hoeffding W. Masstabinvariante korrelations-theorie. Schriften Math Inst Univ Berlin. 1940;2:181–233.
  • Whitt W. Bivariate distributions with given marginals. Ann Statist. 1976;4:1280–1289.
  • Chiu M, Jackson KR, Kreinin A. Correlated multivariate Poisson processes and extreme measures. Model Assist Stat Appl. 2017;12(4):369–385.
  • Grandell J. Mixed Poisson processes. Dordrecht: CRC Press; 1997.
  • Zocher M. Multivariate mixed Poisson processes [dissertation]. Uppsala: Almqvist & Wiksell; 2005. Available from: http://webdoc.sub.gwdg.de/ebook/dissts/Dresden/Zocher2005.pdf
  • Lundberg O. On random processes and their application to sickness and accident statistics [dissertation]. Uppsala: Almqvist & Wiksell; 1964.
  • Cont R, Tankov P. Financial modelling with jump processes. Boca Raton, Fla.: CRC Press; 2004.
  • Feller W. An introduction to probability theory and its applications. Vol. 1. New York, N.Y.: John Wiley & Sons; 2008.
  • Chiu M. Correlated Multivariate Poisson Processes [dissertation]. Toronto: University of Toronto; 2021.
  • Rachev ST, Rüschendorf L. Mass transportation problems: Volume I: theory. New York, N.Y.: Springer Science & Business Media; 1998.
  • Puccetti G, Wang R. Extremal dependence concepts. Statist Sci. 2015 11;30(4):485–517. Available from: https://doi.org/https://doi.org/10.1214/15-STS525
  • Nocedal J, Wright S. Numerical optimization. New York, N.Y.: Springer Science & Business Media; 2006.
  • Devroye L. Non-uniform random variate generation. New York, N.Y.: Springer; 1986.
  • MacDonald Z. A modified simplex method for solving Ax=b,x≥0, for very large A arising from a calibration problem. Computer Science Department, University of Toronto; 2020. Available from: http://www.cs.toronto.edu/pub/reports/na/Zoe_MacDonald_MSc_Research_Paper.pdf
  • Penikas H. Basel IRB asset and default correlation parametrization. Moscow: Bank of Russia, Research and forecasting Department; 2020.
  • Bae T, Mazjini M. Backward simulation of correlated negative binomial Lévy processes. Math Statist. 2019;7(5):191–196.
  • Crump KS. On point processes having an order statistic structure. Sankhyā. 1975;37:396–404.

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:

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:

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.