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 Federico Echenique, Mira Frick, Pablo Kurlat, Juuso Toikka, Rakesh Vohra

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