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No-arbitrage conditions and pricing from discrete-time to continuous-time strategies.

Cherif, Dorsaf; Lépinette, Emmanuel (2021), No-arbitrage conditions and pricing from discrete-time to continuous-time strategies.. https://basepub.dauphine.psl.eu/handle/123456789/22222

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AIP_continu_Journal1.pdf (393.8Kb)
Type
Document de travail / Working paper
External document link
https://hal.archives-ouvertes.fr/hal-03284660
Date
2021
Series title
Cahier de recherche du CEREMADE
Pages
34
Metadata
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Author(s)
Cherif, Dorsaf
Faculty of Sciences of Tunis [University of Tunis]
Lépinette, Emmanuel
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
In this paper, a general framework is developed for continuoustime financial market models defined from simple strategies through conditional topologies that avoid stochastic calculus and do not necessitate semimartingale models. We then compare the usual no-arbitrage conditions of the literature, e.g. the usual no-arbitrage conditions NFL, NFLVR and NUPBR and the recent AIP condition. With appropriate pseudo-distance topologies, we show that they hold in continuous time if and only if they hold in discrete time. Moreover, the super-hedging prices in continuous time coincide with the discrete-time super-hedging prices, even without any no-arbitrage condition.
Subjects / Keywords
No-arbitrage condition; AIP; NFL; NA; NFLVR; NUPBR; Discrete-time financial model; Continuous-time financial market model; Super hedging prices; Pseudo-distance

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