Local martingales and the fundamental asset pricing theorems in the discrete-time case
AbstractThis paper is devoted to giving simpler proofs of the two fundamental theorems of asset pricing theory, in iscrete-time and finite horizon: namely the no-arbitrage theorem, and the market completeness theorem. Some elementary but apparently new results are also given on discrete-time martingale theory, and in particular a new condition for a local martingale to be a martingale.
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 Springer in its journal Finance and Stochastics.
Volume (Year): 2 (1998)
Issue (Month): 3 ()
Note: received: October 1996; final version received: December 1997
Contact details of provider:
Web page: http://www.springerlink.com/content/101164/
Find related papers by JEL classification:
- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
- D40 - Microeconomics - - Market Structure and Pricing - - - General
You can help add them by filling out this form.
CitEc Project, subscribe to its RSS feed for this item.
- Igor Evstigneev & Dhruv Kapoor, .
"Arbitrage in Stationary Markets,"
Swiss Finance Institute Research Paper Series
07-32, Swiss Finance Institute.
- Miklós Rásonyi, 2004. "Arbitrage pricing theory and risk-neutral measures," Decisions in Economics and Finance, Springer, vol. 27(2), pages 109-123, December.
- Tomasz R. Bielecki & Igor Cialenco & Rodrigo Rodriguez, 2012. "No-Arbitrage Pricing for Dividend-Paying Securities in Discrete-Time Markets with Transaction Costs," Papers 1205.6254, arXiv.org, revised Jun 2013.
- Ralf Korn & Frank Oertel & Manfred Schäl, 2003. "Notes and Comments: The numeraire portfolio in financial markets modeled by a multi-dimensional jump diffusion process," Decisions in Economics and Finance, Springer, vol. 26(2), pages 153-166, November.
- Topaloglou, Nikolas & Vladimirou, Hercules & Zenios, Stavros A., 2008. "Pricing options on scenario trees," Journal of Banking & Finance, Elsevier, vol. 32(2), pages 283-298, February.
- Tomasz R. Bielecki & Igor Cialenco & Ismail Iyigunler & Rodrigo Rodriguez, 2012. "Dynamic Conic Finance: Pricing and Hedging in Market Models with Transaction Costs via Dynamic Coherent Acceptability Indices," Papers 1205.4790, arXiv.org, revised Jun 2013.
- Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742 Elsevier.
- Mikl\'os R\'asonyi & Jos\'e G. Rodr\'iguez-Villarreal, 2014. "Optimal investment under behavioural criteria -- a dual approach," Papers 1405.3812, arXiv.org, revised Jun 2014.
- Bruno Bouchard & Marcel Nutz, 2013. "Arbitrage and Duality in Nondominated Discrete-Time Models," Papers 1305.6008, arXiv.org, revised Feb 2014.
- Paolo Guasoni & Mikl\'os R\'asonyi & Walter Schachermayer, 2008. "Consistent price systems and face-lifting pricing under transaction costs," Papers 0803.4416, arXiv.org.
- Pierre Henry-Labordere & Nizar Touzi, 2013. "An Explicit Martingale Version of Brenier's Theorem," Working Papers hal-00790001, HAL.
- Matteo Burzoni & Marco Frittelli & Marco Maggis, 2014. "Robust Arbitrage under Uncertainty in Discrete Time," Papers 1407.0948, arXiv.org.
- Ivan Guo & Marek Rutkowski, 2014. "Arbitrage Pricing of Multi-person Game Contingent Claims," Papers 1405.2718, arXiv.org.
- Pierre Henry-Labordere & Nizar Touzi, 2013. "An Explicit Martingale Version of Brenier's Theorem," Papers 1302.4854, arXiv.org, revised Apr 2013.
- Balbas, Alejandro & Miras, Miguel Angel & Munoz-Bouzo, Maria Jose, 2002. "Projective system approach to the martingale characterization of the absence of arbitrage," Journal of Mathematical Economics, Elsevier, vol. 37(4), pages 311-323, July.
- Yuri Kabanov, 2008. "In discrete time a local martingale is a martingale under an equivalent probability measure," Finance and Stochastics, Springer, vol. 12(3), pages 293-297, July.
- Alejandro Balbas & Anna Downarowicz, 2004. "Infinitely many securities and the fundamental theorem of asset pricing," Business Economics Working Papers wb043513, Universidad Carlos III, Departamento de Economía de la Empresa.
- Napp, C., 2003. "The Dalang-Morton-Willinger theorem under cone constraints," Journal of Mathematical Economics, Elsevier, vol. 39(1-2), pages 111-126, February.
- Kabanov, Yu. M. & Stricker, Ch., 2001. "The Harrison-Pliska arbitrage pricing theorem under transaction costs," Journal of Mathematical Economics, Elsevier, vol. 35(2), pages 185-196, April.
- Irle, A., 2004. "A measure-theoretic approach to completeness of financial markets," Statistics & Probability Letters, Elsevier, vol. 68(1), pages 1-7, June.
- Marcel Nutz, 2013. "Superreplication under Model Uncertainty in Discrete Time," Papers 1301.3227, arXiv.org, revised Feb 2014.
- Alejandro Balbás & Miguel Ángel Mirás & María José Muñoz-Bouzo, 2001. "Projective System Approach To The Martingale Characterization Of The Absence Of Arbitrage," Business Economics Working Papers wb011505, Universidad Carlos III, Departamento de Economía de la Empresa.
- Miklos Rasonyi & Lukasz Stettner, 2005. "On utility maximization in discrete-time financial market models," Papers math/0505243, arXiv.org.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Guenther Eichhorn) or (Christopher F Baum).
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.