Memory-based persistence in a counting random walk process
AbstractThis paper considers a memory-based persistent counting random walk, based on a Markov memory of the last event. This persistent model is a different than the Weiss persistent random walk model however, leading thereby to different results. We point out to some preliminary result, in particular, we provide an explicit expression for the mean and the variance, both nonlinear in time, of the underlying memory-based persistent process and discuss the usefulness to some problems in insurance, finance and risk analysis. The motivation for the paper arose from the counting of events (whether rare or not) in insurance that presume that events are time independent and therefore based on the Poisson distribution for counting these events.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.
Volume (Year): 386 (2007)
Issue (Month): 1 ()
Contact details of provider:
Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/
Persistence; Random walk; Insurance; Markov chains;
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Masoliver, Jaume & Montero, Miquel & Perelló, Josep & Weiss, George H., 2007.
"The CTRW in finance: Direct and inverse problems with some generalizations and extensions,"
Physica A: Statistical Mechanics and its Applications,
Elsevier, vol. 379(1), pages 151-167.
- Jaume Masoliver & Miquel Montero & Josep Perello & George H. Weiss, 2003. "The CTRW in finance: Direct and inverse problems with some generalizations and extensions," Papers cond-mat/0308017, arXiv.org, revised Nov 2006.
- Scalas, Enrico, 2006. "The application of continuous-time random walks in finance and economics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 362(2), pages 225-239.
- Telesca, Luciano & Lovallo, Michele, 2006. "Are global terrorist attacks time-correlated?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 362(2), pages 480-484.
- Pottier, Noëlle, 1996. "Analytic study of the effect of persistence on a one-dimensional biased random walk," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 230(3), pages 563-576.
- Jaume Masoliver & Miquel Montero & George H. Weiss, 2002. "A continuous time random walk model for financial distributions," Papers cond-mat/0210513, arXiv.org.
- Weiss, George H, 2002. "Some applications of persistent random walks and the telegrapher's equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 311(3), pages 381-410.
- Vallois, Pierre & Tapiero, Charles S., 2009. "A claims persistence process and insurance," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 367-373, June.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.