Artikel
Asymptotic synthesis of contingent claims with controlled risk in a sequence of discrete-time markets
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.
- Sprache
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Englisch
- Erschienen in
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Journal: Theoretical Economics ; ISSN: 1555-7561 ; Volume: 16 ; Year: 2021 ; Issue: 1 ; Pages: 25-47 ; New Haven, CT: The Econometric Society
- Klassifikation
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Wirtschaft
- Thema
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Market completeness
Black-Scholes-Merton model
synthesis of contingent claims
- Ereignis
-
Geistige Schöpfung
- (wer)
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Kreps, David M.
Schachermayer, Walter
- Ereignis
-
Veröffentlichung
- (wer)
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The Econometric Society
- (wo)
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New Haven, CT
- (wann)
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2021
- DOI
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doi:10.3982/TE4034
- Handle
- Letzte Aktualisierung
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10.03.2025, 11:42 MEZ
Datenpartner
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Objekttyp
- Artikel
Beteiligte
- Kreps, David M.
- Schachermayer, Walter
- The Econometric Society
Entstanden
- 2021
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