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

Dorsaf Cherif and Emmanuel Lépinette ()
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Emmanuel Lépinette: CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique

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Abstract: 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.

Keywords: Pseudo-distance; No-arbitrage condition; AIP; NFL; NA; NFLVR; NUPBR; Discrete-time financial model; Continuous-time financial market model; Super hedging prices (search for similar items in EconPapers)
Date: 2023-04-24
Note: View the original document on HAL open archive server: https://hal.science/hal-03284660v1
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Published in Annals of Finance, 2023, 19 (2), pp.141-168. ⟨10.1007/s10436-023-00426-1⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03284660

DOI: 10.1007/s10436-023-00426-1

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