A second-order stock market model
Research Article
First Online:
Received:
Accepted:
- 255 Downloads
- 4 Citations
Abstract
A first-order model for a stock market assigns to each stock a return parameter and a variance parameter that depend only on the rank of the stock. A second-order model assigns these parameters based on both the rank and the name of the stock. First- and second-order models exhibit stability properties that make them appropriate as a backdrop for the analysis of the idiosyncratic behavior of individual stocks. Methods for the estimation of the parameters of second-order models are developed in this paper.
Keywords
Stochastic portfolio theory Atlas model First-order model Second-order modelJEL Classification
G10Preview
Unable to display preview. Download preview PDF.
References
- Banner A., Fernholz R., Karatzas I.: On Atlas models of equity markets. Ann Appl Probab 15, 2296–2330 (2005)CrossRefGoogle Scholar
- Bertoin J.: Temps locaux et intégration stochastique pour les processus de Dirichlet. Séminar de Probab (Strasbourg) 21, 191–205 (1987)CrossRefGoogle Scholar
- Fernholz R.: Stochastic Portfolio Theory. Springer, New York (2002)CrossRefGoogle Scholar
- Fernholz, R., Karatzas, I.: Stochastic portfolio theory: an overview. In: Bensoussan, A., Zhang, Q. (Eds.) Mathematical Modelling and Numerical Methods in Finance: Special Volume, Handbook of Numerical Analysis, Volume XV, pp. 89–168. Amsterdam: North-Holland (2009)Google Scholar
- Ichiba T., Papathanakos V., Banner A., Karatzas I., Fernholz R.: Hybrid atlas models. Ann Appl Probab 21, 609–644 (2011)CrossRefGoogle Scholar
- Mosteller F., Tukey J.W.: Data Analysis and Regression. Reading, Addison Wesley (1977)Google Scholar
- Perron O.: Zur theorie der matrices. Math Annalen 64, 248–263 (1907)CrossRefGoogle Scholar
Copyright information
© Springer-Verlag 2012