Asymptotic synthesis of contingent claims with controlled risk in a sequence of discrete-time markets

David M. Kreps () and Walter Schachermayer ()
Additional contact information
David M. Kreps: Graduate School of Business, Stanford University
Walter Schachermayer: Faculty of Mathematics, University of Vienna

Theoretical Economics, 2021, vol. 16, issue 1

Abstract: We examine the connection between discrete-time models of financial markets and the celebrated Black--Scholes--Merton (BSM) continuous-time model in which ``markets are complete." Suppose that (a) the probability law of a sequence of discrete-time models converges to the law of the BSM model and (b) the largest possible one-period step in the discrete-time models converges to zero. We prove that, under these assumptions, every bounded and continuous contingent claim can be asymptotically synthesized, controlling for the risks taken in a manner that implies, for instance, that an expected-utility-maximizing consumer can asymptotically obtain as much utility in the (possibly incomplete) discrete-time economies as she can at the continuous-time limit. Hence, in economically significant ways, many discrete-time models with frequent trading resemble the complete-markets model of BSM.

Keywords: Market completeness; Black-Scholes-Merton model; synthesis of contingent claims (search for similar items in EconPapers)
JEL-codes: D0 G0 (search for similar items in EconPapers)
Date: 2021-01-15
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://econtheory.org/ojs/index.php/te/article/viewFile/20210025/29612/842 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:the:publsh:4034

Access Statistics for this article

Theoretical Economics is currently edited by Simon Board, Federico Echenique, Todd D. Sarver, Juuso Toikka, Rakesh Vohra, Pierre-Olivier Weill

More articles in Theoretical Economics from Econometric Society
Bibliographic data for series maintained by Martin J. Osborne ().