Pricing rules and Arrow–Debreu ambiguous valuation
This paper considers pricing rules of single-period securities markets with finitely many states. Our main result characterizes those pricing rules C that are super-replication prices of a frictionless and arbitrage-free incomplete asset structure with a bond. This characterization relies on the equivalence between the sets of frictionless securities and securities priced by C. The former captures securities without bid-ask spreads, while the second captures the class of securities where, if some of its delivers is replaced by a higher payoff, then the resulting security is characterized by a higher value priced by C. We also analyze the special case of pricing rules associated with securities markets admitting a structure of basic assets paying one in some event and nothing otherwise. In this case, we show that the pricing rule can be characterized in terms of capacities. This Arrow-Debreu ambiguous state price can be viewed as a generalization for incomplete markets of Arrow-Debreu state price valuation. Also, some interesting cases are given by pricing rules determined by an integral w.r.t. a risk-neutral capacity. For instance, incomplete markets of Arrow securities and a bond are revealed by a Choquet integral w.r.t. a special risk-neutral capacity.
(This abstract was borrowed from another version of this item.)
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.
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.
Volume (Year): 49 (2012)
Issue (Month): 1 (January)
|Contact details of provider:|| Web page: http://www.springer.com|
|Order Information:||Web: http://www.springer.com/economics/economic+theory/journal/199/PS2|
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.:
- Gilboa, Itzhak & Schmeidler, David, 1989.
"Maxmin expected utility with non-unique prior,"
Journal of Mathematical Economics,
Elsevier, vol. 18(2), pages 141-153, April.
- repec:dau:papers:123456789/5630 is not listed on IDEAS
- Ross, Stephen A, 1978. "A Simple Approach to the Valuation of Risky Streams," The Journal of Business, University of Chicago Press, vol. 51(3), pages 453-475, July.
- Sujoy Mukerji & Peter Klibanoff and Massimo Marinacci, 2011.
"Definitions of Ambiguous Events and the Smooth Ambiguity Model,"
Economics Series Working Papers
525, University of Oxford, Department of Economics.
- Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2011. "Definitions of ambiguous events and the smooth ambiguity model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(2), pages 399-424, October.
- Luciano De Castro & Marialaura Pesce & Nicolas Yannelis, 2011.
"Core and Equilibria under ambiguity,"
1534, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Bernard Bensaid & Jean-Philippe Lesne & Henri Pagès & José Scheinkman, 1992. "Derivative Asset Pricing With Transaction Costs," Mathematical Finance, Wiley Blackwell, vol. 2(2), pages 63-86.
- Charalambos D. Aliprantis & Rabee Tourky, 2002.
"Markets That Don'T Replicate Any Option,"
Department of Economics - Working Papers Series
832, The University of Melbourne.
- Elyès Jouini, 1999.
"Price Functionals with Bid-Ask Spreads: An Axiomatic Approach,"
New York University, Leonard N. Stern School Finance Department Working Paper Seires
99-038, New York University, Leonard N. Stern School of Business-.
- Jouini, Elyes, 2000. "Price functionals with bid-ask spreads: an axiomatic approach," Journal of Mathematical Economics, Elsevier, vol. 34(4), pages 547-558, December.
- Elyès Jouini, 1997. "Price Functionals with Bid-Ask Spreads : An Axiomatic Approach," Working Papers 97-05, Centre de Recherche en Economie et Statistique.
- Chateauneuf, Alain, 1991. "On the use of capacities in modeling uncertainty aversion and risk aversion," Journal of Mathematical Economics, Elsevier, vol. 20(4), pages 343-369.
- Michael Magill & Martine Quinzii, 2002. "Theory of Incomplete Markets, Volume 1," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262632543.
- repec:crs:wpaper:9513 is not listed on IDEAS
- Erio Castagnoli & Fabio Maccheroni & Massimo Marinacci, 2002.
"Insurance Premia Consistent with the Market,"
ICER Working Papers - Applied Mathematics Series
24-2002, ICER - International Centre for Economic Research.
- Biswas, A. K. & Parthasarathy, T. & Potters, J. A. M. & Voorneveld, M., 1999. "Large Cores and Exactness," Games and Economic Behavior, Elsevier, vol. 28(1), pages 1-12, July.
- Jouini Elyes & Kallal Hedi, 1995. "Martingales and Arbitrage in Securities Markets with Transaction Costs," Journal of Economic Theory, Elsevier, vol. 66(1), pages 178-197, June.
- Alexandre Baptista, 2007. "On the Non-Existence of Redundant Options," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(2), pages 205-212, May.
- Ehud Lehrer, 2005.
"A new integral for capacities,"
Game Theory and Information
- Scott Condie & Jayant Ganguli, 2011. "Informational efficiency with ambiguous information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(2), pages 229-242, October.
- Klaus Nehring & Michael Magill & Julian R. Betts, 2003.
"Capacities And Probabilistic Beliefs: A Precarious Coexistence,"
978, University of California, Davis, Department of Economics.
- Nehring, Klaus, 1999. "Capacities and probabilistic beliefs: a precarious coexistence," Mathematical Social Sciences, Elsevier, vol. 38(2), pages 197-213, September.
- Klaus Nehring, "undated". "Capacities And Probabilistic Beliefs: A Precarious Coexistence," Department of Economics 97-08, California Davis - Department of Economics.
- Stephen A. Ross, 1976. "Options and Efficiency," The Quarterly Journal of Economics, Oxford University Press, vol. 90(1), pages 75-89.
- Bettzuge, Marc Oliver & Hens, Thorsten & Laitenberger, Marta & Siwik, Thomas, 2000. "On Choquet prices in a GEI-model with intermediation costs," Research in Economics, Elsevier, vol. 54(2), pages 133-152, June.
- Chateauneuf, A. & Kast, R. & Lapied, A., 1992.
"Choquet Pricing for Financial Markets with Frictions,"
92a11, Universite Aix-Marseille III.
- A. Chateauneuf & R. Kast & A. Lapied, 1996. "Choquet Pricing For Financial Markets With Frictions," Mathematical Finance, Wiley Blackwell, vol. 6(3), pages 323-330.
- repec:dau:papers:123456789/4721 is not listed on IDEAS
- repec:arz:wpaper:eres1993-121 is not listed on IDEAS
- Clark, Stephen A., 1993. "The valuation problem in arbitrage price theory," Journal of Mathematical Economics, Elsevier, vol. 22(5), pages 463-478.
- Jouini, Elyes & Kallal, Hedi, 2001.
"Efficient Trading Strategies in the Presence of Market Frictions,"
Review of Financial Studies,
Society for Financial Studies, vol. 14(2), pages 343-369.
- Elyès Jouini & Hédi Kallal, 1999. "Efficient Trading Strategies in the Presence of Market Frictions," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-035, New York University, Leonard N. Stern School of Business-.
- Elyès Jouini & Hédi Kallal, 1998. "Efficient Trading Strategies in the Presence of Market Frictions," Working Papers 98-31, Centre de Recherche en Economie et Statistique.
- Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
- Yaron Azrieli & Ehud Lehrer, 2007. "Extendable Cooperative Games," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 9(6), pages 1069-1078, December.
- Han Ozsoylev & Jan Werner, 2011. "Liquidity and asset prices in rational expectations equilibrium with ambiguous information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(2), pages 469-491, October.
When requesting a correction, please mention this item's handle: RePEc:spr:joecth:v:49:y:2012:i:1:p:1-35. 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: (Sonal Shukla)or (Rebekah McClure)
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.