Fundamental theorems of asset pricing for piecewise semimartingales of stochastic dimension
The purpose of this paper is two-fold. First is to extend the notions of an n-dimensional semimartingale and its stochastic integral to a piecewise semimartingale of stochastic dimension. The properties of the former carry over largely intact to the latter, avoiding some of the pitfalls of infinite-dimensional stochastic integration. Second is to extend two fundamental theorems of asset pricing (FTAPs): the equivalence of no free lunch with vanishing risk to the existence of an equivalent sigma-martingale measure for the price process, and the equivalence of no arbitrage of the first kind to the existence of an equivalent local martingale deflator for the set of nonnegative wealth processes.
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.:
- De Donno, M. & Guasoni, P. & Pratelli, M., 2005. "Super-replication and utility maximization in large financial markets," Stochastic Processes and their Applications, Elsevier, vol. 115(12), pages 2006-2022, December.
- Winslow Strong & Jean-Pierre Fouque, 2010.
"Diversity and Arbitrage in a Regulatory Breakup Model,"
1003.5650, arXiv.org, revised Dec 2010.
- Winslow Strong & Jean-Pierre Fouque, 2011. "Diversity and arbitrage in a regulatory breakup model," Annals of Finance, Springer, vol. 7(3), pages 349-374, August.
- Downarowicz, Anna & Balbás, Alejandro, 2004. "Infinitely many securities and the fundamental theorem of asset pricing," DEE - Working Papers. Business Economics. WB wb043513, Universidad Carlos III de Madrid. Departamento de Economía de la Empresa.
- Eckhard Platen, 2006.
"A Benchmark Approach To Finance,"
Wiley Blackwell, vol. 16(1), pages 131-151.
- Y.M. Kabanov & D.O. Kramkov, 1998. "Asymptotic arbitrage in large financial markets," Finance and Stochastics, Springer, vol. 2(2), pages 143-172.
When requesting a correction, please mention this item's handle: RePEc:arx:papers:1112.5340. 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: (arXiv administrators)
If references are entirely missing, you can add them using this form.