We consider a one-period market model composed by a risk-free asset and a risky asset with n possible future values (namely, a n-nomial market model). We characterize the lower envelope of the class of equivalent martingale measures in such market model, showing that it is a belief function. Then, we reformulate a general one-period pricing problem in the framework of belief functions: this allows to model frictions in the market and can be justified in terms of partially resolving uncertainty according to Jaffray. We provide a generalized no-arbitrage condition for a generic one-period market model under partially resolving uncertainty and show that the “risk-neutral” belief function arising in the one-period n-nomial market model does not allow to satisfy such condition. Finally, we derive a generalized arbitrage-free lower pricing rule through an inner approximation of the “risk-neutral” belief function arising in the one-period n-nomial market model.

Envelopes of equivalent martingale measures and a generalized no-arbitrage principle in a finite setting / Cinfrignini, Andrea; Petturiti, Davide; Vantaggi, Barbara. - In: ANNALS OF OPERATIONS RESEARCH. - ISSN 0254-5330. - 321:(2023), pp. 103-137. [10.1007/s10479-022-05126-z]

Envelopes of equivalent martingale measures and a generalized no-arbitrage principle in a finite setting

Cinfrignini, Andrea;Vantaggi, Barbara
2023

Abstract

We consider a one-period market model composed by a risk-free asset and a risky asset with n possible future values (namely, a n-nomial market model). We characterize the lower envelope of the class of equivalent martingale measures in such market model, showing that it is a belief function. Then, we reformulate a general one-period pricing problem in the framework of belief functions: this allows to model frictions in the market and can be justified in terms of partially resolving uncertainty according to Jaffray. We provide a generalized no-arbitrage condition for a generic one-period market model under partially resolving uncertainty and show that the “risk-neutral” belief function arising in the one-period n-nomial market model does not allow to satisfy such condition. Finally, we derive a generalized arbitrage-free lower pricing rule through an inner approximation of the “risk-neutral” belief function arising in the one-period n-nomial market model.
2023
equivalent martingale measures; belief functions; generalized no-arbitrage principle; lower pricing rule
01 Pubblicazione su rivista::01a Articolo in rivista
Envelopes of equivalent martingale measures and a generalized no-arbitrage principle in a finite setting / Cinfrignini, Andrea; Petturiti, Davide; Vantaggi, Barbara. - In: ANNALS OF OPERATIONS RESEARCH. - ISSN 0254-5330. - 321:(2023), pp. 103-137. [10.1007/s10479-022-05126-z]
File allegati a questo prodotto
File Dimensione Formato  
Cinfrignini_Envelopes-equivalent_2022.pdf

solo gestori archivio

Tipologia: Versione editoriale (versione pubblicata con il layout dell'editore)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 582.86 kB
Formato Adobe PDF
582.86 kB Adobe PDF   Contatta l'autore

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1666261
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 4
  • ???jsp.display-item.citation.isi??? 2
social impact