Advanced Search
MyIDEAS: Login to save this paper or follow this series

Self-similar models in risk theory

Contents:

Author Info

  • Krzysztof Burnecki

Abstract

This Ph.D. thesis is concerned with self-similar processes. In Chapter 2 we describe the classes of transformations leading from self-similar to stationary processes, and conversely. The relationship is used in Chapter 3 to characterize stable symmetric self-similar processes via their minimal integral representation. This leads to a unique decomposition of a symmetric stable self-similar process into three independent parts. The class of such processes appears to be quite broad and can stand as a basis of different risk models. In Chapter 4 we give examples of applications of self-similar processes in insurance risk modelling. In Chapter 5 we illustrate a test of self-similarity (namely variance-time plots) on DJIA index data in order to justify the use of self-similar processes in financial modelling. Last but not least we propose an alternative model for stock price movements incorporating a martingale which generates the same filtration as fractional Brownian motion.

Download Info

If 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.
File URL: http://www.im.pwr.wroc.pl/~hugo/RePEc/wuu/wpaper/HSC_98_03.pdf
File Function: Final version, 25 May 1998
Download Restriction: no

Bibliographic Info

Paper provided by Hugo Steinhaus Center, Wroclaw University of Technology in its series HSC Research Reports with number HSC/98/03.

as in new window
Length: 52 pages
Date of creation: 1998
Date of revision:
Handle: RePEc:wuu:wpaper:hsc9803

Contact details of provider:
Postal: Wybrzeze Wyspianskiego 27, 50-370 Wroclaw
Phone: +48-71-3203530
Fax: +48-71-3202654
Email:
Web page: http://prac.im.pwr.wroc.pl/~hugo
More information through EDIRC

Related research

Keywords: Self-similar process; Risk theory; Lamperti transformation; Insurance; Option pricing;

Find related papers by JEL classification:

References

References listed on IDEAS
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.:
as in new window
  1. Furrer, Hansjorg & Michna, Zbigniew & Weron, Aleksander, 1997. "Stable Lévy motion approximation in collective risk theory," Insurance: Mathematics and Economics, Elsevier, vol. 20(2), pages 97-114, September.
  2. Aleksander Janicki & Aleksander Weron, 1994. "Simulation and Chaotic Behavior of Alpha-stable Stochastic Processes," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook9401.
  3. Krzysztof Burnecki & Makoto Maejima & Aleksander Weron, 1997. "The Lamperti transformation for self-similar processes," HSC Research Reports HSC/97/02, Hugo Steinhaus Center, Wroclaw University of Technology.
  4. Weron, Aleksander & Mercik, Szymon & Weron, Rafal, 1999. "Origins of the scaling behaviour in the dynamics of financial data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 264(3), pages 562-569.
  5. Krzysztof Burnecki & Jan Rosinski & Aleksander Weron, 1997. "Spectral representation and structure of self-similar processes," HSC Research Reports HSC/97/03, Hugo Steinhaus Center, Wroclaw University of Technology.
  6. L. C. G. Rogers, 1997. "Arbitrage with Fractional Brownian Motion," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 95-105.
Full references (including those not matched with items on IDEAS)

Citations

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:wuu:wpaper:hsc9803. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Rafal Weron).

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.