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

Dorsaf Cherif and Emmanuel Lepinette

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Abstract: In this paper, a general framework is developed for continuous-time 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.

Date: 2024-05
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Published in Annals of Finance (2023)

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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2405.07713

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